Growing up, we always had a plastic bag full of plastic bags. They had many uses—garbage bags, lunch bags, carrying dirty soccer cleats, etc. Sometimes they got reused once, other times they got reused a lot. They were surprisingly sturdy.
Cloth might be better, but it depends how much energy is required to make the cloth bags.
One particular benefit of cloth bags is they result in less litter.
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.
Same, those cloth/linen bags are indestructible. Can’t remember having thrown a single one away yet and the oldest one I can accurately date is from before the 07/08 financial crisis. They’re also much more comfortable to carry than any plastic bag I’ve seen.
A friend of mine has used an IKEA bag to lug around a dozen or so board games (including some heavy ones) to every game night for years. Those things are incredibly durable.
Cloth might be better, but it depends how much energy is required to make the cloth bags.
One particular benefit of cloth bags is they result in less litter.