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.

Because we don't have term limits.

Under the current system, power flows within the House coalitions based on all the things that go into "ordinary" politics. Bargains, alliances, coalitions based on interest or political support or shared patrons or what have you.

Term limits end up breaking all that. Everyone's going to be gone in ten or twelve years. No one can build a lasting power base. No one can cultivate long-term relationships. When you are first elected, every single person in the House that isn't in your class will be gone for your final two years; and every single other person that will be in the House during those last two years (other than your class) hasn't been elected yet.

That dynamic ends up driving the Legislators into classes, and after a few cycles of this each "senior" class ends up just taking the leadership positions in turn. Since no one can outlast the term limits, no one can build up enough power to disrupt that tendency. It's a mirror of the impact of term limits on running against incumbents; just like there's no reason to take on an incumbent when you know day and date when the seat will be open, there's little reason to try for the Speakership against a more senior Rep when you know they'll be gone next term. Over time, you just end up with the roles landing with the "class" whose turn it is.