I do believe that one could become flexible enough without pain to the same extent. Though not with yoga. I haven't seen many yoga poses that require 90º over-splits. There is no evidence to suggest that muscles don't become flexible without pain at a certain point in time or flexibility. I assume it would just take way too long to ever be acceptable. It would be like landing an axel one year, then taking a year to land a double salchow, then another year for the 2T, then another year for the 2Lo, etc. Way too long to ever be competitive. By the time the skater that's taking a year to get all their jumps has their double axel, they would have aged out of international junior. Same with RG, would take way too long and their career would be over. I don't believe pain to the point of crying is a requirement in most cases.
We also have to be careful to distinguish between types of pain. There's extreme discomfort. I got my needle two years ago (what I believe is called a candlestick in some parts of the world, but that's what my coach calls it) stretching with extreme discomfort. It wasn't pleasant, but it wasn't pain. To anyone who knows the feeling, it was the same amount of discomfort that dancing ballet on pointe is once you develop enough callouses. I then got a hyperextended needle a couple months later. Stretching for that didn't hurt in a bad way, but there was definitely pain involved because I was pushing myself to get it very quickly. Over *********, I stopped stretching the extreme positions I need for my spins and spirals (big mistake). I'm now trying to get the hyperextended needle back because it makes my balance in a regular needle better on the ice. So far no pain involved. Just, as always with extreme stretches, lots and lots of discomfort. There is also the type of pain when something goes wrong, such as when you pull a muscle. This hurts and will continue to hurt once out of the stretch. This is something that should always be avoided, obviously. I'm a figure skater, not a rhythmic gymnast, so obviously I don't do all the moves that they do, but from my experience stretching, pain was only a necessity when I needed to get new moves very quickly. Just my two cents. And wow this is a wall of text.