Which is why I understand pushing to the inhib turret, but if they're turtling OR you have the chance to push an inhibitor turret off an ace or something like that, I feel that taking the bottom one is superior?
Bot lane is usually going to be the farthest from an ace though. In mid-late game, most fights are either at a tower already, or else due to the baron dance. If you get an ace off of a fight by baron, then you're going to want to take baron, and then just push whatever is fastest to push, so that you can get the most advantage out of it. It's better to take an extra tower or the inhib by pushing mid lane than it is to push down one less objective in bottom lane.
If you're sieging a tower, you don't want to do it bot, because that leaves you very far away from Baron, and gives the other team the potential opportunity to 2 man sneak it.