Here's one saying 131 uses [1].
Cotton isnt actually all that green though. And as the article points out plastic bags can be very light weight so aren't that bad. If I were choosing a boogie man, plastic bags wouldn't be top of the list. But I wouldn't be using a reusable cotton bag either.
[1] https://assets.publishing.service.gov.uk/government/uploads/...
Edit: This is actually linked to from the article.
Plus in these situations im reminded of before I had a car, I'd walk to the shops, and not wanting to lug around a load of reusable bags I got disposables and walked home. What's the better option there? Car and reusable bags, or walk and disposables?
Having said all that I'd agree with you.
The better option is that you don't get the choice and you just deal with taking bags with you. "Lugging bags around" is a bit over the top, don't you think? Even the massive IKEA style bags fit in a back pocket.
I used to just bring a big military style backpack to the shop.