Your questions are valid but to fully answer them would require me to write a book, which in fact I have done! If you are keen to learn more about this, check out
Your Body, Your Yoga. In the meantime, I can say a few things; in life -- seek balance! Too much or too little is rarely healthy. You can be too flexible! You can be too stiff. Why do you want extreme flexibility: it is not healthy nor functional. Each joint requires both stability and mobility: if you overstretch the joint, you are making it unstable which means it won't be able to support you in times of extreme stress. Yes, a joint can be too stiff and affect your mobility as well, so seek the
Goldilocks' position.
For example: take the hamstrings. These really should be called the hamsprings! If they are too tight, flexion at the hips can be reduced too much (you can't touch your toes -- but so what?), but if they are too loose, the ability to jump, leap and suddenly explode into extension is lost. Would you want your shock absorbers on your car to be really loose? Too loose and they lose their ability to absorb the shocks. Too tight and they transmit too much as well. Athletes, like basketball players, get their ability to jump high from to the tightness of their tendons and ligaments: the hamsprings and Achilles tendons. When they flex before jumping they tension these tissues and then the recoil from that tension springs back through the legs helping them to jump powerfully. They could not do that if their hamstrings were really loose. I could offer many more examples, but hopefully you get the point.
Very flexible people are more at risk of injury because their joints are less stable than stiff people. Flexible people can ballistically go past the point of their joints' tolerance, and that is where injuries occur. Stiff people will never threaten their joints because they are too stiff and never try to go really deep in any movements. Talk to retired athletes, dancers, gymnasts, etc...they usually have some of the most broken bodies you will ever find! They made a choice between maximizing performance at the expense of health.
Don't seek the maximum, seek the optimum!
Cheers
Bernie