Zoning is about 100 years old, and it's not the reason Manhattan doesn't have enough groceries. And ultimately, market forces almost always win over regulations.
Reformulate the question: why do people tolerate living in dense tiny apartments, without easy access to necessities like childcare and grocery stores?
You don't need tiny apartments to have density. You can do it with smaller single-family houses on smaller lots, narrow one-way streets, and alleyways for parking instead of driveways and garages. This is how the pre-war streetcar suburb of Riverdale, Toronto is designed [1] and it has much higher density than the rest of the city.
[1] https://www.youtube.com/watch?v=MWsGBRdK2N0
> You don't need tiny apartments to have density.
Sure, it starts with "just do row houses" and "missing middle" and in two generations it becomes "we should allow SROs".
> [1] https://www.youtube.com/watch?v=MWsGBRdK2N0
That's a propaganda channel that "conveniently" ignores everything against their narrative.
These kinds of density still require cars. Unless you want to have a stay-at-home spouse who can do full-time housekeeper duty (like in that Toronto neighborhood).
Manhattan doesn't have enough groceries? Do you have a source for that? Everywhere in the city I go has plenty of grocery stores.