I don't think that's right. Just look at Johnson. He's not "senior", but he is Speaker. I believe he's a first-termer.

So one counter-example disproves your hypothesis, if we are speaking in science terms (which I'm prone to do).

Anyone can be speaker. Yes, the senior class will be the ones in their last term. But there is no assurance that they will reach their limit. People get voted out all the time. Not as frequently as they should. Incumbency is a powerful thing. But they do get voted out. Leadership may tend to be chosen from that group, but Johnson proves that it may not shake-out that way consistently.

I rather liked Robin Williams' line that politicians are like diapers; they need to be changed frequently, and for the same reasons. :-)