I don't believe there was a great plan in place, since the overarching strategy in the post-SAF era seems to be for the club to be in CL positions, stay relevant (a cup here and there) and... basically take it from there. It is something that has allowed the current ownership to keep milking their cash cow, with a potential sale always in the cards should the club's commercial lustre takes a hit after several years in the wilderness.
I believe they were more than happy with Mourinho (first United manager to win a trophy in his first season at the club, CL qualification never in doubt in his second year) to ignore all the red flags that usually come with the Portuguese the longer he stays at a club and offer him a contract extension back in January 2018. That, and a bit of United "exceptionalism", the idea that United could offer him the platform to change his ways and be the long-term manager he had failed to become when he held the most prestigious managerial seat in the world or when he was managing the only club he can still call "his own".
In this sense, when Mourinho threw his toys out of the pram, i don't believe they saw the squad or the playing style (focused on counter-attacks) as the problem. On the contrary, i think they were relatively quick with his sacking because he had been open about the team's ceiling (yes, i know, he should also be held accountable for it). They had already decided that a massive overhaul, like the one LvG's attempted, was out of the question, so they wanted someone to build on Mou's first two seasons. I agree that Poch was the "obvious" candidate on the horizon (end of season), but Solskjaer came in and, during his interim run, he (unwillingly) confirmed all their preconceived biases about the team, its direction and its abilities. It was a mistake that Solskjaer paid in the end. That, and a bit of United "exceptionalism" again. Not so much the idea to make a great manager out of an old legend (the dream scenario at every club) as much as the idea that we can turn an ex-legend with very little to show over a decade of managing, into a managerial great.