I would say (and correct me if I am wrong) the reason this is the case other than the "it's just sports", is because in most games, you are supposed to be that singular character and therefore have full control over them. In sports, you can't be every single player, it is SUPPOSED to be a team sport. Therefore if multiple people are playing it, it's possible for one player to make a mistake. We can't have a game where every single player on the field is controlled by a different player, this wouldn't be viable. So you add things to the game to to make it feel that way.
For example, take a shooter game, if you want an arcade experience, you pick up CoD, it isn't realistic and just gives you the illusion you are playing a military shooter. If you want a more accurate representation of real life, you play a game like Arma. Also you can't control every player on the battlefield on your side but they can make everyone on the battlefield a player, if someone makes a mistake it can make things much more exciting. You can't control if another player accidentally gives away your position and puts you in danger and now you have to find a way to make up for it and fight your way out of a precarious position.
Now back to madden, we can't have actual players in every position (no one would ever play oline), so we have to emulate that with ai decisions. If you remove any randomness like botched snaps, it takes the realism away because the ai is not emulating real life by being infallible. I think back to team play and how fun it was to be able to just have 3 players on a team (one for QB, one for WR, and one for HB or another WR). It made the game so fun when you had to weigh how much you trusted the other players not to make mistakes and how much they were able to make big plays vs their likelyhood of turning the ball over.
Edit:
I'd also just like to add that as a huge Dark Souls fan, a lot of people talk about the randomness that happens in that game being unfair; those that enjoy the game like me know that the randomness and sometimes unfair things that happen in that game make for some of the most intense and exciting gameplay I've ever experienced. Is it a game for everyone? No. Can it be super frustrating sometimes? Absolutely. I think Madden could take a page from this. Football isn't a game for everyone, the game should be frustrating sometimes while still being fun, it shouldn't be 100% predictable.
Edit#2:
I'll also add that botched snaps are less in line with Mario not jumping when you press the button and more in line when you press R1 when carrying the ball to protect the ball and your player still fumbles. It happens, I don't hear players complaining that it should be 100% effective that when you cover up the ball it should always work, it simply lowers the chances of putting the ball on the ground. Botched snaps would also go in line with this, as well as failed audibles. The more things you call at the line before snapping the ball should increase the likelyhood of a mistake. As it stands now there is literally no risk to calling 15 audibles before the ball is hiked and sure fake snapping can cause false starts which is nice but it should also sometimes cause a snap while not ready. If you have a high awareness QB, maybe he recognizes it and can quickly recover by catching it and having to collect himself before he can throw it or run where as a low awareness QB would take a lot longer to recover and it results in a fumble.