IN my opinion, the benefits in stretching are so subtle that you don't realise it until you need them.
One of the things I see a lot with older, fast and very fit riders is what I call the cyclist's stoop. I think it has to do with the shortening of certain muscles and ligaments/tendons, including the hamstrings which in turn play havoc with their lower backs.
I have quite good flexibility in terms of looking after my hamstrings and achilles. I also try to keep my side muscles and ITBs stretches to avoid issues with them. And then there are the groin ligaments and muscles. Not important? How do you go getting on the bike?
I know most people here are younger, but trust me, the older you get, the more you appreciate having muscles, ligaments and tendons that are supple. Being able to keep active depends on it, in my experience.
I don't do terribly much to keep them that way. Touching the floor with the palms of my hands a couple of time each time I shower, running my hands down the sides of my legs at the same time, twisting the torso left and right...
I know when things aren't right when my lower back starts to ache, then hurt enough to restrict my movement.