user28350: Naturally, having more time to ponder each move lets skilled players figure out better decisions and avoid errors one might make when there is a pressing time limit, with more time allowing more informed moves.
However, we're also just human, and even the smartest chess players have imperfect memory and ability to envision deeper and deeper decision trees, so at some point the benefits of additional time would become negligible.  In general, how much time per move would be sufficient such that increasing it further would not result in a noticeable improvement at the grandmaster level?
I'd like to focus on just the human computation aspect, so you can ignore fatigue or attention-span effects from spending many hours on a single chess game.

user2001: 
I'd like to focus on just the human computation aspect, so you can ignore fatigue or attention-span effects from spending many hours on a single chess game.

I find this hard, because human capabilities are a big factor in setting time limits for a game.
Let's assume that a GM-level player makes their best move after about 20 minutes of thinking.
40 moves with 20 minutes per move, per player, is 40 * 20 * 2 = 1600 minutes of play, about 26 hours.
A human player is unlikely to enjoy or perform well for longer than 7 hours.
The increment is there so a player has enough time to make their move, press the clock and write down the move on the scoresheet.
To avoid crazy timescrambles where pieces fly everywhere.
To keep time trouble civilized.
Another aspect is bathroom visits. If there was a 30 second increment and then every 10th move you get a 5 minute increment, that move would give you a bathroom break. Now that would increase quality of play, because you can end up stuck at the board playing only on increment while holding back your bathroom needs.
The human body, its capabilities, its needs, are a key aspect for answering this question.
I don't have a better answer than this for now.

28350: <p>Naturally, having more time to ponder each move lets skilled players figure out better decisions and avoid errors one might make when there is a pressing time limit, with more time allowing more informed moves.</p>
<p>However, we're also just human, and even the smartest chess players have imperfect memory and ability to envision deeper and deeper decision trees, so at some point the benefits of additional time would become negligible.  In general, how much time per move would be sufficient such that increasing it further would not result in a noticeable improvement at the grandmaster level?</p>
<p>I'd like to focus on just the human computation aspect, so you can ignore fatigue or attention-span effects from spending many hours on a single chess game.</p>
 2001: <blockquote>
<p>I'd like to focus on just the human computation aspect, so you can ignore fatigue or attention-span effects from spending many hours on a single chess game.</p>
</blockquote>
<p>I find this hard, because human capabilities are a big factor in setting time limits for a game.</p>
<p>Let's assume that a GM-level player makes their best move after about 20 minutes of thinking.</p>
<p>40 moves with 20 minutes per move, per player, is 40 * 20 * 2 = 1600 minutes of play, about 26 hours.</p>
<p>A human player is unlikely to enjoy or perform well for longer than 7 hours.</p>
<p>The increment is there so a player has enough time to make their move, press the clock and write down the move on the scoresheet.</p>
<p>To avoid crazy timescrambles where pieces fly everywhere.</p>
<p>To keep time trouble civilized.</p>
<p>Another aspect is bathroom visits. If there was a 30 second increment and then every 10th move you get a 5 minute increment, that move would give you a bathroom break. Now that would increase quality of play, because you can end up stuck at the board playing only on increment while holding back your bathroom needs.</p>
<p>The human body, its capabilities, its needs, are a key aspect for answering this question.</p>
<p>I don't have a better answer than this for now.</p>
