Having just gone through this there are a lot of factors that play into it. It's really not fun having 11 on the field and 4 dressed on the sidelines.
It's not that there are 15/16 players, it's that during the game kids get dinged. Now you have players in places they have not played (WR is now the FB, the CB is now the Mike), and that can get them hurt, or worse, they get someone else hurt. Moving kids around when you have 25 or 50 players is one thing, moving a players when you have 6 total OL or 2 RB's/LB's is quite another. You can plan for when a player goes down, but when he goes down and now you are making 3 other moves on the fly it gets tough, you end up taking timeouts just to get a playing into a position.
You can't practice with 16 kids. All the drills, exercises, team time, all that stuff is displaced/disrupted because you don't have bodies. Options are to scavenge the JV and/or have them practice with the varsity. Which may help the varsity, but varsity players are varsity for a reason, if the JV's were good competition for the varsity players they would be on varsity. There are things you do (half-line, video, board work, agilities) and things you don't (hitting is out, can't go team, might not be able to go 7-7 or group). But your practice is not what it was.
JV players (parents) aren't coming up. Fear of getting hurt and/or players not being 'mentally ready' to play is most often cited. You can't force a kid to come up and in a lot of places going to the varsity is not the Big Deal it was back before.
Because you have low numbers you have to have everyone able to play everywhere. That means it all has to be very simple. But you don't have the time to teach everyone every assignment and every technique. And the numbers can drop in-game so you are caught. You do the best you can.
Some teams have setup a hard number - 16, 17 or something, for whatever reason(s) their numbers drop, where if they are at/below that number they cancel. That's a discussion that the coaches don't want to have, "we'll play with 12...", but it should be a number that is determined before the season gets started, and communicated to the AD/administration.
And the numbers can drop, a lot, without warning. Meaning you have to adjust to all this on the fly. Not a good situation these days.
And this is not just the bottom feeders that are getting hit. Some bigger programs are dropping Frosh or JV programs, etc. 8-man is really starting to get some discussion over dropping the program. Too many things are counting on home football games for schools to be willing to give up football.
And the "Smart Thing" above - It's different when you have 15-16 kids vs. 40 kids. What is smart/acceptable at 40 players is not smart at 15 players. The odds of getting hurt change with the number of players.