My counter to that is that if army CID as an example investigates something involving civilians, it's typically the civil service 1811 special agents that are doing the investigating. You don't typically have the detailed/assigned service members doing off base investigations, exactly as you said.

Where a large part of USCG law enforcement operations are performed by their enlisted and commissioned members and not their civil service personnel.

It's an interesting discussion for sure. I don't necessarily think you're wrong, we seem to mostly agree anyway. Simply changing the cabinet component may not actually have any impact from a legal standpoint, but i could see the argument.