There isn't a market failure in groceries in NYC. There's a huge number and diversity of stores, and profit margins are as low as anywhere else in the world. Also, of course, see the sibling comment who is complaining about grocery stores while using Amazon Fresh. There's a competitive delivery market.
Of all of his policies, I actually don't really care if he wants to try to put some grocery stores in grocery deserts. It probably won't work, but whatever.
Really depends on where you are in the city; I used to shop at Whole Foods on the UWS and it was lovely, and when visiting this past summer my friend and I visited both the Bowery Whole Foods and the Wegmans near Astor Place and zero complaints with either of them.
But TBH I don't think the grocery deserts he's looking to service are going to be anywhere near where the average HN user lives.
The market failure in NY is due to the local government, so clearly the local government stepping in to offer a replacement is the solution. On an unrelated note, I have a bridge to sell you.