I don't mean to be one of those "but, well" people, but, well, in my experience it hasn't been. I've not had a car for quite some time and still carry luggage and groceries. The added fitness from walking more has probably helped quite a bit.
It is a very common sight to see people in my neighborhood get on a bus with one of those square rolling carts with a week's (or more) worth of groceries. I've considered doing the same thing but between my spouse and I, we can fit everything we want in our two backpacks and two to three reusable handle bags.
Lots of how we run society is for the collective good. Strangely, transportation seems to be the opposite. We subsidize the hell out of individual transport while minimizing collective, more efficient transport. What most of us who advocate for public / group transport want is for those to be more even.