Seems to me that the most likely path is shambling towards hard brexit.
Boris Johnson becoming PM would surely make that outcome substantially more likely.
It's not exactly 'white male privilege', because the vast majority of males are white here, but it's certainly 'white, upper class elite private school, male privilege' that means someone with the record of amateurism, failure and carelessness that BJ has could float so easily to the very top.
If someone like Khan were to completely flush down the toilet £40million+ of tax payers' cash on an improperly-tendered vanity project that never even got built, that would surely wipe out any tiny chance he had of getting to Number 10. But the 'garden bridge' fiasco doesn't seem to even slow Johnson down. Never mind his unedifying stint as foreign secretary. Only someone on the higher end of as many axes of privilege as BJ could build a political career out of repeatedly resigning from top jobs that he wasn't very good at and then being given better ones.
(I don't even rate Khan very much - he's too timid and inactive as mayor in my opinion - but he's never cocked-up anything anywhere near the scale that Boris Johnson has)