Medical usage is often necessary. Why not just start with things that are completely extraneous, like packaging, bottles, etc.
I live in a county that's enacted one, and it's been unambiguously an improvement for the area on top of the core goal of "reduce plastic waste". But visiters look at me like I live in East Germany when I mention that.
I don't say this to discredit the idea, but it's politically treacherous, and not a lot of people are willing to stick their necks out for the right thing.
The level of inconvenience added to my life by not using plastic bags is so unbelievably small it's not even worth the oxygen I would need to spend to express my discomfort. It's really, really not a big deal.
The fact that some people are extraordinarily high-stress and enjoy making problems out of nothing should not be our concern. Let's not optimize for those people, they'll never be happy anyway.
The problem is, sometimes you do need them because you had to change plans and didn't bring any bags. I don't own a car or anything where I can leave them. Often leave the house without even a backpack.
And paper bags don't work when it rains or when you need to bring heavy stuff like drinks.
And my water, I buy it in 6-packs of 2L, they come plastic-wrapped with a handle so you can carry them more easily. The tapwater in my city is not drinkable.