The rules are made by the party, and the party can change those rules. It has before and it will again.
In this case however I think it's much more likely that if Khan is the choice, room will be found for Khan to win a byelection somewhere. Labour has plenty of London MPs still, they've struggled mostly with the North, progressive policies sell very well among socially aware people inside the M25 but aren't popular among people for whom the whole point was that the Unions ought to run the country.
In lots of Labour seats in London it really wouldn't matter who you run. That's why Vauxhall's MP used to be Kate Hoey. Nice part of London, very gay friendly, many of the people there have never eaten meat, much less gone fox hunting and of course they opposed Brexit - and yet of course Kate was pro-hunting, pro-guns, anti-gay and fiercely favoured Brexit. Why did they elect her? Because it said "Labour" next to her name and they don't do research.