Well they did just watch those protestors also beat up several cops and kill one of them, so I doubt that endeared them either.
The Joint Chiefs already wrote that Biden as going to be the CiC come 20th. The election was legitimate. You seem to have this odd idea that the military as a whole is so weak that they'll throw democracy into the trash because of hurt feelings. They are professional people. They'll protect the ideals that your country stands for and its laws. One which includes the right of people to say nasty things about them and even argue for less money to be used on the military. It's okay to do so. And they know it. Naturally there are some members here and there who will show this to be untrue in their cases, but I'm speaking more about them as an organisation here.
I'll concentrate on thee military side here a bit more as I'm still part of the reserves here, but for about the police... the video doing their job seems to involve getting thrown to the wolves more often when said video shows the police lied about events in their reports.
And there's been plenty of looking into the voting issues. You just don't seem to like what those checks have shown, or rather, haven't shown. Paper ballots have been checked against electronic and cases of fraud have been found, showing that the system does work. There was just now a new case of a campaign worker who was caught for fraud. The cases are few and in national elections, not big enough to affect the results. I'd expect the danger of these is more relevant in local elections where 10s of votes could already swing results.
So why would the military or cops join in with armed protestors? If those armed protestors actually tried to change results by force, the insurrectionists would be dealt with by them.