Robots that can fold anything might be useful in an industrial cleaning or textile manufacturing setting, but it would compete with humans who can do that in seconds. For towels, there's specialized machines (and have been for years): https://www.youtube.com/results?search_query=towel+folding+m...

towel folding doesn't seem like a step towards automating clothing, any more than building a tall ladder is a step towards ladders tall enough to reach the moon. Anyway https://ruthtillman.com/post/all-clothing-is-handmade/

Getting computer vision and physics models to correctly handle fabric is the hard part of automating what's left in textiles.

Everything else is ultimately just inclined planes and a power rod pulling on levers, which is the stuff that was solved with the Jacquard machine and a whole industry of competing models of sewing machine before we even had electricity let alone electric servos.

I think at the root textiles just don't go where you want them to go the way, say, a rigid object or a fluid does.

There are a lot of active research areas. So far progress hasn't been happening. I don't know if it is because the problem is unsolvable (likely), or we are not investing enough into it to solve them (also likely).