Around 160,000 people who are mostly white, mostly male, mostly wealthy and mostly elderly and mostly anti-trade union ARE going to choose the next prime minister.

And quite rightly too.
The populace elected a Conservative government, and the Conservatives have a system for electing a leader.
If Labour were in government they would expect to be allowed to elect their own leader. Last time they did so (although not in government) they elected Keir Starmer. The time before they elected Jeremy Corbyn. Somewhat earlier the rank and file had no choice because Blair appointed Brown.
Yes, I know that in between Labour had Harman (acting) Milliband, and Harman (acting).