Parking meters still impose a cost on the preexisting residents and are not a wholly entrepreneurial solution since they require cooperation from the city.
Parking permits could work if they are granted in perpetuity to whoever currently resides in the preexisting residences, but a) somebody still has to pay for enforcement, b) I've never heard of a parking permit system that actually worked that way, and c) it is also a government, rather than entrepreneurial, solution.
Besides, why solve the problem in a way that must be managed in perpetuity when you can solve it once and for all by just making the developer build enough parking in the first place?
(By the way, I'd like you to know that I'm not making these arguments because I'm a fan of automobile-centric development -- quite the contrary! Rather, I merely take issue with the idea of letting the developer do whatever is "fiscally optimal" for himself without considering the rest of the community that would be impacted by the result.)