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.
As someone who lives in cities and has never owned a car, doing just fine here with walking my groceries back weekly and taking luggage around when I travel thanks very much. Doesn't work for everyone but that's why we have suburbs and plenty of car first/primary cities like Houston or Portland.
Around half of NYC residents don’t own a car. In Manhattan 3 of 4 don’t own one. Luggage bags have wheels and lots of older people have small wheeled carts for moving groceries, etc. more easily.
Movement of all but the rarest, large items is not a problem.
I have had absolutely no problem lugging my luggage to the airport or carrying my groceries on foot or by mixed foot/train/bus. It might require some modifications to your trip (e.g., going more frequently, or purchasing some personal shopping carts to carry stuff around in), but it's not that hard.
Depending on area of course, but usually a grocer or supermarket is much closer, meaning that more frequent and smaller trips aren't an issue and mean you often have fresher produce to work with.
Ride-hailing apps now make that point moot, as do on-demand car rental services like Zipcar and car2go. Nonetheless I've never had a problem getting groceries on and off the bus.
