DoD contract, currently.
I was on a smaller team when I was private side and we definitely did more and touched more things. I think part of my issue is I'm far too specialized now as an ISSO. No real variety. Holding out for a full time remote gig, if possible. But, here in the Springs much of what's available is DoD.
The problem with downsizing too much is one runs into the issue of being overworked/underpaid for it. Ideally, if I stay in IT (which probably will be the case, regardless of my random pining for swinging a hammer), I'd be with a company that's large enough to provide some variety without spiting Peter to pay Paul.
In general, if a team is handling everything, they're really sys admins who are letting security slip or doing the bare minimum at best. The private company I left after the M&A had just stood up their security team a few months prior to me hiring on. Reason? They previously had been handling security the way you described, and it was just inefficient. So the guy who had been treating security as an additional duty was able to convey the reasons *why* that was such a bad idea.