Boxing is probably one of the only sports that I can think of off the top of my head, where you don't have to be good to be a professional...Plain and Simple! In every other sport, whether it be Basketball, Football, Baseball, Hockey, you have to work your way up the minor leagues or college, get drafted and then make it to the Pros. Not boxing, anybody and I mean anybody can get a boxing license and become a professional. Therefore, you see a lot of out of shape boxers stepping in the ring!
Don't even compare MMA, where they fight 3 round matches and compare it to boxing? That's why you see these MMA guys run into each other like **** fighters blowing their load in the first couple of minutes. The rest of the time, they are wrestling on the mat and if you don't think that much of that is resting, then you're a fool. MMA is a sprint, boxing is a sport that you need not only muscular endurance, but explosive power too!
That's not the real reason why we see out of shape boxers fighting though. There are many guys getting around wearing or challenging for title belts that are overweight. It's not just the tomato cans getting around with their stomachs hanging out.