he objectively did do better with that squad
look at the PL PPG in the 6 months either side of the switch
at the time of his sacking, almost mid way through the season, Poch had three PL wins, Jose managed that in a fortnight
Forgive me, did I miss something? Did we qualify for the CL at the end of that season? Did he get us through any CL knock-out stages? He did not do better by any measure (other than your three win metric).
Here's a run of results for you!
Dec 28th 2019 - Norwich h - 2-2
Jan 1 2020 - Soton A 0-1
Jan 11 - Liverpool H 0-1
Jan 18 - Watford H 0-0
We then won three games on the spin, then lost two games on the spin, then covid.
FWIW, mid-November is (by my calculation -and I am a brick maths man so hold me to it if I am wrong!) is 3 months in. Let's give it an extra couple of weeks and say 3.5 months in. Mourinho had more than half a season.
It is ground nearly as old and pointless as my claims to have been the Glenn Hoddle of Kingston back in '81, but Poch dealt with a lot of brick in that final season+, including being 'homeless' for an extra two-thirds of a season, not getting the cycle of players he wanted at vital times, and ultimately being baited and switched in summer 2019 - Nov 2019.
Mourinho said he could do better with that squad. He never did. That's a fact.
(n.b. not that I need to say this as I am sure it is clear, but I have never, ever liked him, thus any accusation of confirmation bias, or just plain bias against the fudging prick, is absolutelky fair and I accept it...I still think the facts bear me out BUT yes, I don't like him and that must influence me somewhere...)