user27380: Why do chess puzzles need a unique solution?
This is different from real games, where such situations do occur, but more frequently, there are multiple avenues to success. Contrary to what one might think, that makes chess puzzles easier, not harder! I have solved countless puzzles only because I knew that there is one and only one solution and therefore could exclude moves that I would have needed to consider in a real game.
Especially in some cases, where there are multiple different mates, all solutions should be accepted. Adding such puzzles in a set would lead to better and more realistic training.
Also, practical positions may be added where the task may be to play until a certain evaluation threshold is reached or held for a certain number of moves against an engine.
Why is tactical training today so "unrealistic"?

user23501: Puzzles are usually intended to be hard or at least challenging. Puzzles with multiple solutions tend to be easier since one can arrive at one though multiple avenues. People who design or choose to present puzzles  don't want puzzles that are trivial. So the result is that most tend to have one unique solution.

user33363: I can think of one puzzle that doesn't and can't have a unique solution, but which of the two possible solutions is correct and which is wrong depends on information that can't be derived from the board itself. It's from Smullyan's "Chess Mysteries of Sherlock Holmes" the chapter "Thoughts of a Logician", so I guess it falls under

Article 8 - Author's Solution
Every chess composition must be capable of being solved only by the author's solution. Special features of the author's solution (such as multiple solutions or setplay in helpplay problems) should be expressly stipulated.


user8860: Basically for the same reason that we're not impressed by a win by
queen sacrifice if there was also a pedestrian one- or two-move mate.
There are chess problems that deliberately have more than one solution,
often to complement each other in some way.  This usually happens in helpmates
(which are probably of little or no interest to players seeking "training")
but they're occasionally seen also in direct-mate problems.

user33358: I'll have to disagree with the premise here. They don't need a unique solution.
For a matter of fact, some Chesstempo tatic puzzles have sub-optimal solutions, but if they still reach a treshhold evaluation (+-1.5 if I recall correctly) you won't fail or pass the puzzle; Instead a blue box will tell you that although that is a winning move, you should keep trying finding the best one.

user33362: Don't look at chess puzzles as a way of training for competitive chess. Chess problems are a genre of their own. A good chess problem is a piece of art.
By requiring a unique solution we place an extra constraint on the puzzle, making it more valuable. This constraint makes it even more difficult to craft a nice puzzle, and we appreciate that.
See https://sportstar.thehindu.com/magazine/chess-problem-an-art-form/article29710563.ece

user4418: 
Why do chess puzzles need a unique solution?

Because those are the rules. The governing body, the World Federation of Chess Composition, sets the rules. Their latest Handbook of Chess Composition includes a Codex where the rules are laid out.
Here are the relevant articles:

Article 8 - Author's Solution
Every chess composition must be capable of being solved only by the author's solution. Special features of the author's solution (such as multiple solutions or setplay in helpplay problems) should be expressly stipulated.
Article 9 - Cook
A chess composition is called cooked if it has a solution that differs in its first move from the author's solution.
Article 10 - Dual
A dual is said to occur if, after the first move, there is more than one method of satisfying the stipulation.


user8201: If someone says to me: "Let's meet at (mumble) on (mumble)", I may respond: "Sorry I didn't catch that."
Tactical puzzles and artistic problems are both (in different ways) about communicating a message, and if the solution is not essentially unique, then the message is unclear.
Uniqueness then becomes a thing in its own right. In a puzzle, it can simplify the automated response, which can just focus on a single line. In a problem, it becomes an aesthetic property: how wonderfully unlikely in a certain position that the correct sequence of moves is unique!
It's perfectly valid (and fun!) to use the property of uniqueness to prune the search space when solving. Solving is a way to learn and appreciate, and difficulty of solving may be a virtue in both puzzle and problem. However this difficulty is subordinate to the nature of the solution. I can legitimately profit (although less) from a puzzle/problem by just reading the solution.

27380: <p>Why do chess puzzles need a unique solution?
This is different from real games, where such situations do occur, but more frequently, there are multiple avenues to success. Contrary to what one might think, that makes chess puzzles <strong>easier</strong>, not harder! I have solved countless puzzles only because I knew that there is one and only one solution and therefore could exclude moves that I would have needed to consider in a real game.</p>
<p>Especially in some cases, where there are multiple different mates, all solutions should be accepted. Adding such puzzles in a set would lead to better and more realistic training.
Also, practical positions may be added where the task may be to play until a certain evaluation threshold is reached or held for a certain number of moves against an engine.
Why is tactical training today so &quot;unrealistic&quot;?</p>
 23501: <p>Puzzles are usually intended to be hard or at least challenging. Puzzles with multiple solutions tend to be easier since one can arrive at one though multiple avenues. People who design or choose to present puzzles  don't want puzzles that are trivial. So the result is that most tend to have one unique solution.</p>
 33363: <p>I can think of one puzzle that doesn't and can't have a unique solution, but which of the two possible solutions is correct and which is wrong depends on information that can't be derived from the board itself. It's from Smullyan's &quot;Chess Mysteries of Sherlock Holmes&quot; the chapter &quot;Thoughts of a Logician&quot;, so I guess it falls under</p>
<blockquote>
<p>Article 8 - Author's Solution</p>
<p>Every chess composition must be capable of being solved only by the author's solution. <strong>Special features of the author's solution (such as multiple solutions or setplay in helpplay problems) should be expressly stipulated.</strong></p>
</blockquote>
 8860: <p>Basically for the same reason that we're not impressed by a win by
queen sacrifice if there was also a pedestrian one- or two-move mate.</p>
<p>There <em>are</em> chess problems that deliberately have more than one solution,
often to complement each other in some way.  This usually happens in helpmates
(which are probably of little or no interest to players seeking &quot;training&quot;)
but they're occasionally seen also in direct-mate problems.</p>
 33358: <p>I'll have to disagree with the premise here. They don't need a unique solution.</p>
<p>For a matter of fact, some Chesstempo tatic puzzles have sub-optimal solutions, but if they still reach a treshhold evaluation (+-1.5 if I recall correctly) you won't fail or pass the puzzle; Instead a blue box will tell you that although that is a winning move, you should keep trying finding the best one.</p>
 33362: <p>Don't look at chess puzzles as a way of training for competitive chess. Chess problems are a genre of their own. A good chess problem is a piece of art.</p>
<p>By requiring a unique solution we place an extra constraint on the puzzle, making it more valuable. This constraint makes it even more difficult to craft a nice puzzle, and we appreciate that.</p>
<p>See <a href="https://sportstar.thehindu.com/magazine/chess-problem-an-art-form/article29710563.ece" rel="noreferrer">https://sportstar.thehindu.com/magazine/chess-problem-an-art-form/article29710563.ece</a></p>
 4418: <blockquote>
<p>Why do chess puzzles need a unique solution?</p>
</blockquote>
<p>Because those are the rules. The governing body, the <a href="https://www.wfcc.ch/wfcc-about/hcc/" rel="noreferrer">World Federation of Chess Composition</a>, sets the rules. Their latest <a href="http://www.sci.fi/%7Estniekat/books/hcc8.pdf" rel="noreferrer">Handbook of Chess Composition</a> includes a Codex where the rules are laid out.</p>
<p>Here are the relevant articles:</p>
<blockquote>
<p><strong>Article 8 - Author's Solution</strong></p>
<p>Every chess composition must be capable of being solved only by the author's solution. Special features of the author's solution (such as multiple solutions or setplay in helpplay problems) should be expressly stipulated.</p>
<p><strong>Article 9 - Cook</strong></p>
<p>A chess composition is called cooked if it has a solution that differs in its first move from the author's solution.</p>
<p><strong>Article 10 - Dual</strong></p>
<p>A dual is said to occur if, after the first move, there is more than one method of satisfying the stipulation.</p>
</blockquote>
 8201: <p>If someone says to me: &quot;Let's meet at (mumble) on (mumble)&quot;, I may respond: &quot;Sorry I didn't catch that.&quot;</p>
<p>Tactical puzzles and artistic problems are both (in different ways) about communicating a message, and if the solution is not essentially unique, then the message is unclear.</p>
<p>Uniqueness then becomes a thing in its own right. In a puzzle, it can simplify the automated response, which can just focus on a single line. In a problem, it becomes an aesthetic property: how wonderfully unlikely in a certain position that the correct sequence of moves is unique!</p>
<p>It's perfectly valid (and fun!) to use the property of uniqueness to prune the search space when solving. Solving is a way to learn and appreciate, and difficulty of solving may be a virtue in both puzzle and problem. However this difficulty is subordinate to the nature of the solution. I can legitimately profit (although less) from a puzzle/problem by just reading the solution.</p>
