If memory serves, Dan Jarvis also did it, being both MP and mayor of the South Yorkshire city region or whatever it was called at the time.

It is fairly innately political. No Prime Minister has ever polled as low as Starmer and come back from it, or so is being said in the press. Burnham might be a smart electoral move, but he's not a plaything of the Labour right, so they kept him out.

The rules are inconsistent. You can be Mayor of Sheffield and an MP at the same time but you can’t be Mayor of Greater Manchester and an MP.