I understand what you are saying, but when things are going badly wrong (for example, when we had a disastrous December, when we could barely score a goal and any number of negative records which were broken), it is upto Giggs to speak up and tell LVG some home-truths. Now if LVG does not listen...it's on LVG. But the assistant needs to assist his manager. LVG will sometimes bounce ideas off his assistant. If he keeps his mouth shut when things are going tits up or LVG suggests a bad idea, that's not much of an assistant.
Of course, we don't actually know for sure, whether or not Giggs did (or didn't) speak up.
In any case, I'd much rather Mourinho bring in his own team with which he is comfortable and he believes he can win trophies with. I'd love for our GK coach to have stayed, but Jose will no doubt bring in people he is comfortable with.
At the end of the day, we want results and it's on Jose to deliver these results.