Require, no but if they want to play they better be there.I'm pretty sure there are regulations on what the coaches can "require" the players to do in the off season. For instance, the coaches can't require the QBs, WR and DBs to get together three times a week in the summer for 7 on 7 work. They can heavily recommend it. I'm not sure what extent the regulations go as far as weight training...etc.
So, to say, "These coaches need to make these kids get in the weight room" I'm pretty sure technically that would be an NCAA violation.
Now, maybe the regulations have changed over the years but I'm pretty sure it is still that way.
On my FB team players had to be at 30 lifting sessions during the summer conditioning workouts or they did not play in the first game of the year. There were very few exceptions given. Our starting QB did not play in the first game of the year one year because he did not meet this minimum criteria.
Others are right, I am sure that players are required to be in the wt room and doing conditioning. Some will work harder than others, and they will see the benefits. You hope that players see how Abdulla, Cross, Spencer Long, etc. have made themselves better FB players in the weight room and want to emulate that.
You would be surprised how little time some players have actually spent in a wt room before they get to college. Skill players in particular aren't real big on putting a lot of effort into the wt room in HS. Just my observation and opinion.