Check out this Canadian talking about his grocery trip in Amsterdam: https://www.youtube.com/watch?v=kYHTzqHIngk.
In much of the USA, your produce would freeze and thus become mush.
In much of the USA, temperatures well above 90 degrees would wilt your produce. Also, all your frozen food would be ruined.
If you're carrying frozen food, we have bags with insulation and reflective foil on the inside. Put your frozen food there and even in +40C weather it will take much more than 15 minutes to thaw. Besides, buses and obviously the metros are acclimatized to a temperature of more or less 25C.
It really is just a non-issue. I assure you your produce are left outside for more than 20 minutes. There is no impact at all on freshness, and walkable cities promote smaller grocery stores that tend to have fresher food.
Food grows outside, in direct sunlight, exposed to scorching heat or near-freezing temperatures. Most of the plant based food is still living in the shelf when you purchase it, and has imune systems to fight-off bacteria and the like that would otherwise colonize it. The only concern are products of animal origin in the heat, but even the most sensitive like refrigerated fresh fish, still needs at least a few hours in hot weather before they can become problematic.
When grocery shopping frequently, you're also going for five or ten minutes instead of two hours, and the grocery is probably on your way home.
This has never been a problem for me. Many fresh fruits and vegetables will easily last for a week in your refrigerator (some for longer), and fresh fish or meat can be frozen for later use. Fruits such as berries that degrade rapidly can be eaten first, and fruits that last longer, such as apples or oranges, can be eaten later. Fruits like peaches or avocados can also be bought in varying states of ripeness, which means that different ones could achieve ripeness over the course of a week.
Back when I lived across the street from a grocery store I'd sometimes go get food for dinner, talk a bit with guests for what we wanted for desert, then walk over and pick up whatever we'd decided on. When the grocery store is across the street it is basically an on-demand food pantry.
Living in a dense city like SF is great for somethings, but it sucks when you want to leave, and paying almost $400/month for parking isn't good either. Both lifestyles have their advantages and I think it really comes out to personal taste and choice.