They do get stuck, but mostly as younglings. Their claws are perfect for climbing but not so great for going down, unless the cat realizes it has to do it “backwards”. When they are young I assume that when they reach their target spot, they soon realize that climbing down will be very sketchy since they do it the same way they got there (ie, head first) and start panicking.

I had two cats we had to “rescue” once or twice from trees as kittens and both ended up getting pretty good at climbing down as they grew older.