The "political class" of an anarchical state as I've described would be rotational.

We in the United States have "Jury Duty", where the average citizen is required by law to be selected to be part of a "jury of peers" on legal cases if the defendant exercises their right to a trial by jury.

Jurors can be struck down (relieved of their duty) for many reasons in the jury selection phase by attorneys, the judge, or submitting documentation on why they can't perform their duty.

A corollary compulsory service or duty could be applied to the positions in the three branches of government we have in our current constitutional structure.

We would effectively shift from being a constitutional federal republic (on paper; in practice, the current form of government is a plutocracy) to a constitutional aleatory republic. We would have representative governance, but they'd be subject to review, competency approval, and votes of confidence.

One could also imagine ranked-choice voting and mandatory direct referendums regarding crucial policy decisions. Lobbyists must present their legal proposals to jurist-representatives and the general public, mitigating the efficacy of monetary influence in political speech and advertising.