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I do think so. You seem to be forgetting a rather large proportion of cyclists who don't 'race' or 'train'. I'm not talking about temporarily tight hammies, I'm talking about 20 years at a desk, decides to get fit and do the Ride 100 or an Ironman or something. Racers if they're anything like me will likely have adapted their position over years and probably done some stretching during this time. Even including racers, without an idea of the rider's flexibility, how can fitter can't decide to prescribe stretching or not? How do they know they will need to readjust the rider in a month or two? Things like hamstring flexibility (touching toes or doing a seated measured slide out) are pretty simple ways of indicating a baseline or measuring change, ie. if the rider has increased their range of movement with a stretching routine they've been given.
As for the lower back thing - tight hamstrings cause the pelvis to rotate back which does what? That's right, put strain on the lower back. I stretch hamstrings when I have a sore lower back and it works quite well.
I don't think so. I mean if they're super-tight from racing or training yes, but that will pass and most cyclists get tight hamstrings from riding in position, they're adapting innit. What lots of riding won't sort out is tightness in the hip from hard muscles around nerves that'll mess with the top of the pedal stroke (and other things).
I think for more people the limiter for getting low for TTs etc is in the lower back. Lots of riding can help that. And the right genes.