My guess would because the president is also technically the chief law enforcement officer? Not saying I like it, but that’s how it is I think.
Impeachment is what exists to hold presidents accountable, and then voting is what holds the senate accountable, when they choose not to hold the president accountable.
I think the president can be prosecuted for criminal offenses though when they’re out of office, since what I said above would no longer apply.
This is all correct. The issue is that we've gotten in the mode of not prosecuting our political enemies once they're out of office. That's actually a very important political precedent that has largely served us well. The peaceful transfer of power from the Federalists to the Democratic-Republicans was a huge deal in 1800 and it guaranteed that subsequent transitions (mostly) followed the same model. The problem is, there were no tripwires: what was too far for a president to go? Ford pardoned Nixon, which may have been the right move at the time (I'm mixed), but it became mixed up with the peaceful transfer of power tradition and basically was interpreted as a free pass.
I think we may be about to see the the end of the tradition of get out of jail free cards for former presidents, but I don't know what the long term consequences will be.
Impeachment is what exists to hold presidents accountable, and then voting is what holds the senate accountable, when they choose not to hold the president accountable.
I think the president can be prosecuted for criminal offenses though when they’re out of office, since what I said above would no longer apply.