I think you're right and for one reason: Antonio Conte.
Conte was jobless and practically begging for the Manchester United job (A few months after winning Serie A with Inter) whilst Solskjaer's United were getting battered by Leicester & Liverpool.
Those defeats were fireable offences, it was over at that point but they let him limp on in the job until they were beaten by City and then smashed by Watford.
Conte had signed for Spurs and was already starting to get a tune out of a side looking like they were going into terminal decline.
I think if they hired Conte and gave him the backing Spurs have given him, they'd have turned it around incredibly quickly.
But they'd never hire someone as abrasive as Conte. Levy and Spurs want to win things and actually give a shit about football, Manchester United is basically a bank for an NFL Franchise and a Billionaire family.