To answer your first paragraph, Pochettino's USP is the way in which he projects a certain ype of leadership which transcends the training pitch, to the point whereby he would often by the club's main PR. He is also a manager that has built his methodology on cloear principles: work ethic, no primadonna attitudes, one-for-all-and-all-for-one and not limiting yourself ("you must always have belief" etc). Redknapp from a purely principled leadership angle doesn't come close. So when Poch himself starts seemingly going against HIS OWN principles and says "trophies actually are not important", "i might leave and go elsewhere if we win our first trophy under me" he takes himself down towards Redknapp's levels, who was himself nowhere near as principled as Pochettino but publicly flirted with leaving us and takijng his eye offf the ball and, well, we know the rest.
If anything i judge Pochettino more harshly because of the principles he has that Redknapp didn't.
The second paragraph: i'd much rather Poch turn it around tbh, because A) this is now his squad and has been moulded in his image, for better or for worse and B) i simply don't trust the FOOTBALLING ambition of Levy and the board to actually get a manager who would be able to take to a higher level than the one Pochettino has taken to.
I haven't seen many signs that Pochettino is able to turn things round tbh - and i am still less forgiving in general given his outbursts - but one can only hope today is finally a turning point (though i thought that after Palace....)