Houses contain a lot of soft surfaces such as upholstery, bedding, and carpeting on which a claw(s) can get stuck and cause sever damage if the cat "freaks out" in order to free itself. That's the primary reason to trim.Why would a cat need his/her nails trimmed? Makes no sense.
It's funning to watch a cat grab is back leg and start gnawing/pulling on their claws in order to remove the older sheaths. I find the sheaths on the floor all the time. Now as cats age they do a worse job at maintaining their claws because they lose flexibility.
I've never heard of claws curling back into their pads. That must be breed specific.