Wouldn't it be great if you didn't have to vote for the least horrible candidate? If you could vote for who you wanted without feeling like you're throwing your vote away?
If we had ranked choice voting, we'd have better legislators in office to start with. And if they used it in the speaker votes this could be resolved already.
You're right, because voting for speaker is more charged/personal, I could see it not working. See my other comment here, the idea isn't that a democrat or independent would win, just that you'd have a less bonkers candidate or at least wouldn't be deadlocked.