Some will have an attitude that's there no such things as too many squats, deadlifts, and benchpresses. Build strength and endurance, don't worry about looking "cut". Others want to turn your physique into something fit for a fitness magazine. The reality is chances are different positions have different training needs.

Squats done to full depth develop strength. Lighter weight to shallower depth can build explosiveness though. As you get farther from the where the ball is snapped, explosiveness becomes more important for cuts, acceleration, and pure speed. If your a nose tackle and main job is to eat up the center and the guard so the backer can make a tackle, pure strength and endurance is more important.

Stretching out and developing good joint openness I think helps build as much resistance to injuries as anything, but also so does improving "gross motor" coordination. If you get caught and hit in an awkward posture, you're more likely to get hurt. If you have the body control to stay out of a bad position, you protect yourself more. There are exercises that condition muscle memory to move more efficiently so you don't get turned all wonky.

All that to say - there isn't a one-size fits all approach to S&C. I think the best trainers are the ones that understand a player's performance needs as well as his current body state and can tailor a program for the guy to follow.

Last thing also is diet - you are what you eat. S&C'ing is 80% good diet and nutrition, and rest/sleep. Without them, your body never gets the chances to really recover/grow..