There is actually one "logical reason", that is if you do not want your opponent to be able to muck their cards in order to see what they were holding.
This is one of the reasons there should be an asterisk nest to this rule. Basically if you bet because you have to, you should have the option to see your opponents folded cards.
Sorry, but IMO this isn't even
close to a good enough reason to suspend or change the rules about betting the nuts or mucking.
If someone chooses to fold to your river bet, then they should have the right to muck their cards unseen
regardless of what you're holding. You bet, they folded. You haven't paid to see their cards, so you don't
get to see their cards.
Suggesting that you should be entitled to the benefit of extra information in addition to the benefit of having an unbeatable hand is... well... greedy is probably the most charitable way I could describe that. It's having your cake and eating it too.
Changing the rules to allow you to check so that you can see their cards would be even more problematic, because then every softplayer and angle shooter in the world would just say they were checking "to see what the other player had".
The idea that you'd even want to do that is a bit wonky to me too. I mean the only time you'd even want to consider doing it is because you know your opponent has a hand so bad that there's exactly zero chance that they'll call. First of all, it's not possible to know that with 100% certainty. Second, if you did somehow know that, then how much do you really gain by knowing
exactly what garbage they had? And third, since you can't know that with 100% certainty, surely you're better off putting a bet out there for the times when you're wrong and they do have a hand that can call. Even if it's only 1% of the time it's still +EV.
And while it's true that some card rooms
might enforce this rule differently between cash games and tournaments, I can't think of any good reasons why they should. Again, if your card room doesn't enforce this rule, whatever format you're playing, it's a good idea to ask why. And consider playing somewhere else, because they're basically endorsing collusion and softplaying.
The only time I can think they should even make an exception to the rule is when the nuts is the five cards on the board (so it's obvious to everyone that it's going to be a split pot) and the rake cap hasn't been reached yet (so players would effectively be losing money by betting / raising)