Absolutely there was (some) logic to hiring Jose and Conte at those times; certainly the 'not bothered about trophies', 'not acting like a big club' accusations of the board were curtailed in the immediate short-term..
The problem was then that they were shown to have been very much short-term hires just for those purposes rather than actually trying to show there had been a growth in terms of how the club acts etc: as i've often said before there's little point (or logic) in getting a 'win now' manager only to act like you still have a Pochettino in charge.
Anyone with a football brain knew that Jose had been backed a Man Utd and Chelsea and still crashed and burned (likely because his methods werer being found out more and more at the levels we say we aspire to, i.e. challenging for top trophies, getting top 4, getting to latter stages in europe etc). What did we think we would do differently with Jose that the previous two big clubs couldn't/wouldn't?
Within a couple of months of joining us, Kane was injured long-term on new year's day and Jose publicly said he needed a number 9/target man to function. Never mind how much that shows him up as a coach, we didn't get one for him, even on loan and instead got Stephen Bergwijn, who seemeingly fell into our laps via his agent and the fact he wasn't going to renew his contract with PSV. Good player in or of himself, but again this is the sort of thing that happened when we were under previos managers like Poch...if we'd ALSO got a target man/number 9 then that would have been fine, but alas...and remember this was BEFORE Covid.
Then in the summer of 2020, it was reported on here by
@Grays_1890 that the flurry of transfer activity in the latter part of that transfer window (i.e. when we bought Bale, Regulion, Rodon etc) only happened because the hierarchy saw how we fared in our opening game loss at home 1-0 to Everton. So they assumed all was good in the squad before that. Again, reactionary and totally clueless on the actual footballing state of things (again, ignoring Jose's shortcomings as well...as i say if you are going to hire Jose you should KNOW what it entails in terms of backing).
We know how things turned out with Jose's sacking (the poor timing of doing this) then the nonsense of ending up with Nuno after many weeks of searching...i won't go there now.
We then fired Nuno and hired what looked a REAL coup in Conte, though again one that would need the club to act like how HE would expect them to, i.e. backing him to the hilt fully.
To be fair i think they mostly did: i can't imagine the club would themselves buy the likes of Richarlison and Perisic for the fees and wages they did if not directed to by Conte.
Similarly, they bought Spence when they KNEW it wasn't a Conte pick and they SHOULD HAVE KNOWN that RWB was a position of such importance to how he/his teams function - we saw how things basically broke down a bit when Doherty was injured for the rest of the season and we seemingly got saved by Arsenal's late choke - and to not prioritise signing a rwb that Conte ACTUALLY wanted again showed they were a) not clued up with the football side of how we were playing under Conte b) not clued up with how Conte had got his success historically and c) still acting like Poch was still here...
To be clear, in my opinion they should have prioritised a rwb that Conte absolutely wanted rather than a 'club signing' for the future. We could, after getting such a Conte player, have also got Spence and then sent him out on loan to further his career, make himself better for use by Conte in the future.
The Conte meltdown, i think, started from this point. Yes, Conte was childish in how he eventually melted down, but was this really any different from how he did at his previous clubs (save for the lack of trophies)?
Again, we seemed to hire 'win now' coaches without fully committing to change to acting FULLY in the 'win now' way these coaches would have wanted/expected.
It's the transfer actions around these last two 'big' coaches, together with the timing of sacking Jose before the league cup final, that makes it look like their main strategy is about 'winging it' to get through the current football crisis of any given time rather than having an actual strategy for THFC to be the best FOOTBALL-WISE that it can be.
I also think the veneer of the owners/board actually having good knowledge of how to succeed football-wise has vastly slipped. They have A LOT of work to regain a reputation as even competent football-wise this summer.