With that logic, we should just ban poor people from breeding as well. After all, they are not as well equipped to do it.
A static price is not a prevention, but a disincentivization. Enabling people to do something they are otherwise economically incapable of doing is how we got the 2008 recession. Granted this is a whole different level, but the point is the same. A functioning economy reflects the value, not the means. And as a result, some are less able than others. A price point that makes it difficult for someone to afford a pet will (presumably) make them think twice before taking on a responsibility they might not be able to handle.
If what somebody learnt from life is that "they have to pay for poor people's kids", then indeed some are better for all of us to not have been born in the first place. But those are not necessarily the poor people's kids.