Activist politics are the product of the Board of Supervisors and the school board for the same reason that activist politics are more popular in the House than in the Senate: the boards are elected district-by-district, and don't need to tend to the views of larger masses of people. They answer to a small group of constituents, and that's it. If you have a small voter pool, being an outspoken, controversial activist helps (as long as you don't cross the specific lines your district cares about): it raises your profile because you're controversial, and since you don't need to please everyone, you're more free to say or promote ideas that many other people — who aren't in your district! — view as outrageous.

You don't really need cabals to explain it. And it's unclear to me what mechanism the cabals supposedly have to choose the mayor; why they'd choose London Breed over say, Angela Alioto (a member of the "old money elite"); why they can choose the mayor but failed to choose their desired DA in the same election cycle; etc.