Assuming you had lost all sense and sanity, and mistook the vagaries of football for a narrative that you needed to move on, I would suggest a career working as a columnist for a UK newspaper. However, for the sake of thought exercise, let's do this:
Replacing Pochettino asks two questions.
1) is the current Spurs team/idea of play working?
2) what is the idea of play that we need to win these games that we're currently losing?
1) We spend around 50-66% of our rivals in the table, but have achieved 3rd, 2nd, and possibly 3rd or 4th, We're consistently punching above our weight and getting results beyond what spending levels suggest we should be able to expect. That leads to a follow-up question of is that us kicking ass, or richer clubs fucking up? I think the answer is: both.
We're playing CL-quality, 80-points a season-level football. Richer teams are not, but that is completely separate from our own work. So, broadly, yes, the team and idea are working.
2) What do we need to do to win the games we're losing?
Better subs, better pre-match PR from ourselves (Mauricio talking down the Cups needs to stop) have been mentioned. Being able to stay focused for 90 minutes with no mistakes (unlike the Juventus match) is another. Other than that though, honestly, not much. Sometimes random shit happens and you lose even when you're the better team. Sometimes the other guys just have the game of their lives. That does happen, and shouldn't be used to claim we're not doing the business.
I think, given the pattern of Levy's managerial appointments, that there is a Spurs style in his mind, and that any manager would need to match that. I think that means a short-passing possession game, with a lot of attacking intent, and probably a lot of pressing on top of that. In other words, anyone who comes is going to have to be a Pochettino clone, because that is the "house style", regardless of anything else.
They'd also need European experience and an ability to rotate the squad to preserve fitness.
That narrows the list considerably. There are maybe 5-6 guys who fit that profile, and all of them are currently employed at other clubs. With the exceptions of Pep, maybe Klopp, and maybe, maybe Tuchel, none of them are actually higher profile, or "better" than Pochettino at all.
In other words, there is no case for Mauricio leaving. Giving him additional resources to help learn about rotation and maybe some extra tactical ideas that he could experiment with would be smart, but that's it.
Time to double down with the one that brung us.