For me, it’s not about carrying the groceries, but the mental and temporal overhead of thinking about what I needed, making a list, walking however many additional minutes, spending 15 minutes shopping/paying/packing, etc would strike me as a terrific waste if done daily.
I used to do that when I interned in Germany. The market was near the bus stop and our dorm had limited fridge space, so I’d tend to buy and eat the same day (and rarely cook from scratch). That wouldn’t work so well to feed a family of four that way.
With a folding rolling cart or a bike with good panniers one could easily do all of that for the family of four with minimum hassle with one or two shopping trips a week, plus irregular trips to stock up on bulk stuff like toilet paper.
I think part of the disconnect here, though, is that you're associating this process with extra mental overhead, but when there's no extra effort needed to just get stuff you don't need to think about it as much. Forget to get butter? Oh well, you can literally just get it the next day on your way back from the park or the movie theater—or if you really need it right now, you can get it at corner store just a few blocks away at a slightly higher price.
In my house in the Netherlands, we feed a family of four each day and buy food an hour or two before we cook it precisely because we can't handle the mental overhead of planning food more than 24 hours in advance. ;-)
I used to do that when I interned in Germany. The market was near the bus stop and our dorm had limited fridge space, so I’d tend to buy and eat the same day (and rarely cook from scratch). That wouldn’t work so well to feed a family of four that way.