I've seen estimates that cloth bags are like 100x+ more resource intensive. I doubt that most people get 100 uses from cheap cloth bags.

Of course, there's another option. There are cheap durable bags.

IKEA plastic bags are close to literally indestructible and cost $1USD. Although the smaller version ($0.89) is probably better for groceries. https://www.ikea.com/us/en/p/frakta-shopping-bag-large-blue-...

IKEA might not be great for the environment overall but these bags are an insanely good win. Essentially infinite reuse. Unless you're dragging cinder blocks around in them I'm not sure how they'd ever really wear out.