I can think of two reasons.
One, sadly, you have disallowed, which is the legroom answer.
But what if the answer actually is about legroom?
Since I don't have enough room for my knees, I have to straighten my legs, which requires me to put my feet under the seat in front of me.
It seems to me that if passengers were supposed to put bags under their own seat, people would be fighting over that space more than they already are.
The other reason is safety.
That space has a bar to keep the things in there from sliding forward in a crash.
This serves as a barrier between the space and the occupant of the seat above.
If the bar were at the back of the seat instead of the front, it would allow things to fly into the aisle between the rows, injuring passengers' feet or impeding their egress.
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The gymnastics required to put your bag behind your feet in such a small space would be very interesting.
Bending forward and sliding it in, sure that works.
But pushing it back when you can't see and your legs are in the way?
Most people are not good at bending into pretzels in 31" of space.
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Inconveniencing yourself never creates an argument.
Inconveniencing others, does however.
If you were to put your bag under your seat, you would be affecting the comfort of the passenger behind you.
That passenger may not even have brought a bag on board, but now finds their comfort dependent on the whims of the passenger in front of them.
I think it's easy to see what the result of this is: complaints, arguments, fights, passengers being thrown off the flight.
This does nobody any good.
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The Life Vest Putting your bag underneath your seat could be an obstacle if you had to grab the life vest in case that there were troubles on the flight.
http://main.victorofrank.com/wp-content/uploads/2015/12/140730105130-airbus-a350-14-horizontal-large-gallery.jpg
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In the event of a crash anything on the floor will slide forward.
Having a bar at the front edge of your seat prevents bags from coming to rest against the seat in front and allows a clear space to evacuate your row.
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If you are traveling in flight for longer journey then you will feel difficulty at your base in stretching your legs properly as the bags are already beneath everyone's seat..
safety is also the main reason behind this..if you put your bag below your seat then there is probable chance of stealing your bag with someone else and you will not even get any idea about this..
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I think it's simply a lesser of two evils situation.
If the space is under the seat in front of you, you have the option to use it as storage or leg room.
If it's under your seat, there would be a bar at the back of every seat to prevent the bag from sliding into the passenger behind you.
With a bar at the back of every seat, no one gets any extra leg room.
I guess you could put your feet under your own seat in that case, but that doesn't sound very comfortable to me.
The current arrangement gives people the opportunity for a little leg room in the place that is most comfortable for most people.
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On airplanes, they tell you to put your bags either in the overhead or under the seat  in front  of you. Considering that the front row doesn't have a seat in front of them, and the back seats don't have anything under them, would it not be more efficient to have people put their backs underneath their own seats?  Please don't give me an answer about legroom. We all know airlines don't care about our legroom.
Why do airlines not have you put your bag underneath your own seat?
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<air-travel><hand-luggage><factoids><aircraft>
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Legroom is a big reason, since you would be affecting the comfort of the passenger behind you if you could put your bag under your seat. This also reduces the chance of theft, as well as preventing the bag from flying forward in a crash or blocking the life jacket under your seat. There are a lot of reasons that state this idea would be inefficent ranging from discomfort to safety hazzards. Examples include, a lack of leg room, holding uncomfortable positions for extended durations, theft and potential obstructions to life vests. 
A lack of comfort makes this idea very inefficient. This stems from a number of reasons such as, lack of leg room, the inability to bend into a pretzel and maintaining awkward positions for extended lengths of time. This idea can be a major safety hazzard for a number of reasons i.e in the event of a crash anything under your seat will slide forward, your bags could be an obstacle in the even you need to grab your life vest and there is even the potantial of theft.