We've kinda covered the relevant topics ad nauseam but the bolded is the key IMO. There's some real young talent in the squad (namely Romero, Ben10, Richy, and Kulu), but like you said, that's not enough to take top 4 convincingly even when paired with Kane and Son. Conte is surely gone at this point, but the club really do need to settle on a philosophy in order to stop throwing good money at the bad. While they did back Conte respectably (except in defense and keeper), a manager of his ilk is never going to stop making demands. Conte is probably the most petulant manager and publicly demanding re transfers in the world, but I don't think it would be materially different in terms of demands from Flick, Lucho, Ancelotti, Simeone, etc. Moreover, with those managers (with the possible exception of Ancelotti), like Conte they also have very specific player types in mind, and that's gotten us into tricky situations with player recruitment.
So if we believe (as I do) that Spurs are never going to be the type of club that spend big in every transfer window a la City, United, Chelsea, Newcastle, and to a lesser degree Liverpool, then they need a 'project' type of manager who can build towards a title challenge every 2-3 seasons, as opposed to a philosophy of challenging every season. More importantly though, Spurs need to find a manager who will play attack-minded football that will entertain, because ultimately that's what's most important to Spurs fans, all the better if they can do it at a high level.