If you don't like grocery stores gamifying or selling junk, regulate those aspects. Or put the taxpayer money towards something useful like building public housing.
Food deserts exist in NYC, and many New Yorkers buy staples at corner stores that charge significantly more than a standard grocery store. Your second paragraph implies that this policy is due to some dislike of existing grocery stores, but that assumes these communities are actually being currently served by grocers at all
A perfectly competitive market requires the following (this is not everything, just some):
- Supply perfectly meets demand (yep already wrong here)
- Marginal costs equal to average revenue (this means there should be effectively 0 profit for the seller)
- Zero transaction costs
- Zero externalities (can't exist)