So I'm a manager at a non private institution. At my grade we don't get over time pay, but it's generally just work your job. I always try to claim back time I've worked above and beyond. So I'll finish early sometimes or take a long lunch etc. I tell my team to do the same thing, and those entitled to over time, I pay over time. I was chatting to a colleague outside my area today and it's a super busy time for her right now. I said 'you're gonna claim the time back right?' And it hadn't even occurred to her. Hopefully, I have made her do so in future!
We actually work in a good sector outside USA so get 31 days of leave a year plus public holidays, and full paid sick leave. Also very unionised and protected. BUT, and I say this as someone that is a bit of a workaholic, I don't wanna work for free. I'm claiming that time back as much as possible. People need to adjust to respecting their personal time too.