Flexibility training makes football players less susceptible to injuries Here is report from test done on infantry training. If your discipline is about explosive moves, short, fast runs - think about flexibility, as solution to limit injuries. Another source - abstract, with many references is accessible for free.
Other point spotted by Michael C. is limited range of motion. When exercises are performed at the edge - power goes down, also proper posture can be compromised. That can lead to injury.
I can't confirm that it has significant influence on total power. It can limit injuries, it can make my moves from the edge of range of motion, but that is all. On the other hand - it makes all stabilization muscles working. If they ware not used, then it can be an issue. So at start of stretching - expect significant drop of weights lifted.
Separate topic is how to stretch:
Static stretching. Particular position is taken for some time - longer then a minute. From my personal experience - that should be done on separate training session. Doing normal training gives enough load to my muscles, static stretching after that can double soreness, recovery.
Dynamic stretching. Used sometimes as pre-workout. Fast moves, used to warm body, activate neural system, a bit higher blood pressure. I can't recall exact source but for sprinters that was the only beneficial stretching in terms of speed. When they ware asked to do full stretch before training things went wrong.
Rollers / mobility. Instead stretching, devices are used to press particular points/parts of muscles. To relax, remove tension. Works for me - after workout. That can be used as pre workout as well. Instead slow 20 moves do 10 much faster.
- Ballistic stretching. Old school exercises. From time to time I see runners doing it. Sometimes people are against it, some loves it. If someone can listen to the body - worth to try. Saw it, and decided to try - very good to open hips. I'm doing it from time to time, when upper body is trained. So that is the only exercise that deals with hips, well maybe except running.
As a very side note - I need to collect all the sources... Going back to them is quite problematic. Sorry for that.