It’s my understanding pretty much anyone came be made Speaker.
And FYI...the Speaker has to be VOTED in, by the members of the HOUSE!
Add to the above, just WHY would Chuckles EVER give up being the SENIOR SENATOR FROM N.Y.and his senior positions on all of the Senate committees he's on, to get DEMOTED to the House? Simple answer...HELL WOULD FREEZE OVER, TRUMP WOULD BE MADE KING OF THE USA, WITH COMPLETE POWER, before what you suggest would happen.
I’m not sure what the exact rule is. I believe it has to do with having been in the house previously or in when voted on. Unless a senator was in the house previously or not may matter. But no senator would step down to do it. The reps are there for 2 years and the senators run every 6. Nasty may lose bigly but Chuckie can’t save her. The Dems are on the highway to Hell and there’s no stops. This is a breaking point for them and may be the crossroads for a civil conflict for each side and I believe we all have made our choice.