I think it may be part of a fee to reduce how often people do it. Just imagine if 10% of passengers brought their dogs, just because they could. On a full 737, you're looking at what, just over a dozen dogs on every flight? Going by the "law of really big numbers" you're going to get a lot more noisy dogs for everyone else (and with dogs, that stuff can be contagious ), a greater likelihood of accidents (time, money, and most importantly delays in getting that cleaned up) and a lot of other unintended consequences that can arise from having a dog on board less than rarely.

And as the summary above mentioned, there is technically a limit to the number of animals that can go on a plane. When I was at SkyWest, we were told 1 animal in the cabin at a time, but that could also be waived with the PIC's permission (which supposedly happened more often than not).