Allegri coached for quite a few years before showing much. Conte also had a bit of a mixed bag resume for some years.
Not being desperate to get the head job doesn´t necessarily mean much. For all I know there are personal reasons for it (kids growing up or whatever). And it doesn´t mean he couldn´t be a very good manager when given the chance. The best coach in Norway at the moment "retired" some years ago and was selling cars before he went back to management.
Allegri was manager of Milan by age 43, having been first allowed to run his own team age 36. In between he promoted Sassuolo to Serie B for the first time in their history, and lead Cagliari to their best finish in fifteen years. (He'd lost his first five games in charge with Cagliari, yet the notoriously impatient Cellini stuck with him. Even a stopped clock, etc.).
Conte undertook the transition from assistant to head coach age thirty-seven. Middling as his CV was prior to Juve, he'd earned promotions to Serie A with two different clubs. Juve put him in charge aged 42.
I'd suggest each man illustrates my point that it's unlikely a real talent won't receive the chance to run his own team until he's past fifty, whether or not that talent immediately pays dividends.
As for possible mitigating factors in Shakespeare's delayed ascent, Leicester is in the East Midlands of a small country- a lot of clubs would be within driveable distance for a man who didn't care to uproot his family from their home. (By the bye, Shakespeare followed his guiding star Pearson to Hull- a conspicuously less accessible city).
And while you may not think it means much if someone isn't desperate to win a head coaching job, I'm bound to remark that the people who become football coaches are the real obsessives- either thwarted would-be players, or ex-pros who can't live without the game once they're obliged to call time on their playing careers. As such, the notion that Shakespeare acquired a previously non-existent desire for a top job when he was past the age of fifty doesn't wash with me.