That media/frenemy onslaught is going happen either way. But if he pre-emptively strikes, that is the only major battle front he will be fighting, and he has the goods on why they should be fired, which Nixon didn't. But if he waits, he will have that same battlefront, plus the battlefront of whatever BS that Mueller tries to trot out, most likely being completely trumped up charges on illegally obtained evidence. So he would have twice the fight on his hands.
This is of course assuming that Trump and Mueller haven't agreed on some eventual cease fire, so they can both leave with their dignity intact, which can't be completely discounted. But if they are truly at war, and war is hell, the sooner he can get it over and move on to the MAGA agenda, which by the way includes firing deep state agents such a Mueller anyway, the better.
The sad truth is that there is only one way to avoid a death-match with the media and both parties on one side and Trump on the other. That way is to let the Mueller witch hunt play out. Afterward Trump can fire Sessions and Rosenstein on the same day—and I’d guess he will.
Btw, Nixon had something Trump doesn’t have: a semi-sane, somewhat rational electorate. Post-modernism has triumphed since then, and insanity is the order of the day. Sports Illustrated wouldn’t have put a mutilated male on its cover in Nixon’s day, and called it a woman. Today they do so with almost zero pushback—and that’s just one small example.