dude, 90% of team culture is the kids. if the kids decide they want to run before the season starts, it happens. my team, way it worked, the best kid would start up early, and he'd ask the rest to go run with him. the kids who wanted to hang with him or saw the value did it. zero coach involvement. what you can do is nudge the kids to plant the seed it's worthwhile. if they have the bug, they will start doing any of it. if they get super serious, your plan gets done. otherwise, it's not that you need to cut people because the culture is bad, it's you have failed to soft sell the value of your concept.
my experience harsh iron glove style exercise of power with cuts tends to result in players more at odds with the coach in their daily efforts than concerned with preparing for the game/meet next weekend. you want the kids thinking, i want to be ready for this meet and kick butt and what do i need to do, to do that -- when doing practice. if they are instead thinking about i hate my coach, the effort is probably second rate and they lose the task at hand.