Yeah that's the thing, you're not
meant to need "mass transit" to get
groceries. It shouldn't even be a single "stop" away, it should be even closer. Are you saying you don't have a
single decent grocery shop within a 5-10 minute walk of your house? A 15 minute city is meant to have that. And not just one shop ... you're meant to have
lots and lots of them.
In the last place I lived, there were at least six I could walk to conveniently. And that wasn't a big bustling world-class metropolis either, it was a fairly unspectacular inner suburb of Sheffield[1], a city of 550,000, solidly middle of the pack on most social/economic rankings compared to other UK cities. The closest to "mass transit" was a tram that came three times an hour, but I never took the tram to get food.
I've linked the Streetview of the main high street[2] near where I lived, don't want to dox my exact address but I lived somewhere within a 1 km radius of this point[3]. I could get 98% of my monthly needs from this one street. You can explore the different directions on Streetview to see what I'm talking about. Look at the amenities nearby: cafes, coffee shops, greengrocers, hairdressers, newsagents, liquor shops, nurseries, daycare, schools, a gym, churches, pubs, a bus station, furniture shops, banks, a park, a dentist, pharmacies, several GP practices, a supermarket, hardware store, drycleaners, fast food, probably more that I've forgot, all within a short walk of this point. There's even the start of a pleasant walking trail through the Rivelin valley a bit further to the southwest (a godsend during the lockdowns). And this kind of high street isn't unique, there are plenty such high streets dotted around in the adjoining neighbourhoods: Middlewood, Crookes, Kelham Island, the lot. Most people in the city can walk to one. In fairness it may not meet the "15 minute city" definition since most workplaces are in the city centre so a walking commute takes more than 15 minutes. But hey, the tram is about that quick, and biking doesn't take much longer, 20 minutes maybe. And of course you can drive too; plenty of cars about.
Another example: when I was a student my house was in a 1 km radius of this point[4]. It's clearly suburban, but look at all the amenities. Easy, no "mass transit" needed to buy milk. And now I live within 1 km of this[5] point, exact same thing. It's not even the only such high street I can walk to; there's another about the same distance in the opposite direction from my house. British high streets have overlapping walking-distance radii that jointly cover almost all the suburban parts of a city, on top of the big central shopping district of the city-proper.
Having lots of groceries in walking distance is not a high a bar to clear. The examples I gave are all second- or third-rate cities, unimpressive in most respects; they're not the ones urbanists always talk about like Amsterdam or Copenhagen or Tokyo or anything fancy like that. It takes no particular conscious government policy to make this happen, it just happens on its own, because there's more than enough market demand. Look at the houses, they're almost all 2 storeys, only a few apartments in the 3-4 storey range, and hardly anything taller than that; the places I showed are not very densely populated, yet they support all this business. If your city is big and dense enough to have "mass transit" (I'm assuming a subway or high-frequency surface rail?), it ought to have grocery shops even more densely distributed than where I've lived. If not, it sounds like something has gone very wrong! That just shouldn't happen. What land-use regulations/laws are preventing it?
This is what I meant when I said people use the same words to mean different things ... all kinds of confusion. Best to use Streetview and give examples.
[1] https://en.wikipedia.org/wiki/Hillsborough,_Sheffield
[2] https://en.wikipedia.org/wiki/High_Street
[3] https://goo.gl/maps/6h6qSdFcn2thifM9A
[4] https://goo.gl/maps/HQy3Lens5nqv54fY8
[5] https://goo.gl/maps/5DphPFeKdcJVkNyb8