I don't think the screaming and yelling in the media would have ceased for weeks if Ramsey had been left in the game long after the outcome was certain, and he got injured and missed time.
It's not that I think that's why McVay did it; it was logical to bench Ramsey at that point for his own good.
Ramsey is a firey, passionate competitor and never wants to come out. It's McVay's job to assert himself even if it leads to some visible disagreement with the player. Disagreement is NOT disrespect. You can bet that the other team leaders would straighten Ramsey out if he carried some kind of a grudge against McVay on this matter, going forward. McVay was 100% right; Ramsey 100% wrong.
Sometimes leaders have to suffer having those they lead get mad at them. But, if the leader was right and handled it reasonably well, then respect will come from it. Not to worry; this was probably nothing more than heat of the moment.
And BTW: I saw McVay clearly getting on Stafford's case about something, and Stafford kind of pushing back. Nothing big, but it was plain to me when I saw it. Then after the game a clearly perturbed McVay... grouchy as I recall having ever seen him in public.... expressed his unhappiness with the O. Later Stafford came to the mic and when asked about some things that didn't work out... including some clock problems and the herky/jerky O, and the slow starts.... his response was that this is the NFL and no one ought to expect otherwise.
I think McVay has decided that the only way the Rams are going to get to the Superbowl is if he pushes this team hard... ala the never satisfied Bellicheck. And, BTW, I agree whole heartedly with McVay's criticisms.