It's a LOT of work. There are 11 Board of Supervisor members, 7 SFUSD Board Members, and numerous additional local elected supervisory positions. On top of that, elections being elections, you need to make alliances with Interest Groups that will rally voters to your candidate. All this takes a lot of time and money which has little impact outside of this 49 square mile rock on the Pacific Coast. You could better use that time (the most expensive part) and money to have an actual impact at the State or Federal level, which can have an actual lasting impact. Also, people forget how insular and parochial SF is because it's a smaller city by US and California standards: within California, Los Angeles City is 3.8mil, San Diego City is 1.3mil, and San Jose is 1mil - while San Francisco is barely 800k, roughly comparble to the City of Seattle or City of Charlotte, NC. You almost never hear about Seattle or Charlotte city politics despite both being equally as dysfunctional and sharing similar issues.
> he might have trouble finding anyone to support in local politics
Money speaks.
Why else would Bernie Sander's protege and Donald Trump's former protege turned rival kiss the ring of the exact same billionare.
For example, all SF Progressive politicians de facto HAVE to stump at an (imo extremely overpriced) cafe called Manny's (they have OK hummus, but Oasis Grill across the street is way better and a fraction of the cost), owned by an ex-FB lobbyist and personal friend of Zuck named Manny Yekutiel. And SF city politicians are fine taking money from Marc Benioff even though Salesforce has massive contracts with ICE and the DoD. If the other local business tycoons who live in SF actually cared enough about SF, they'd be playing a role in the local politics as well.
But, as they don't due to time constraints, what ends up happening is Old Money Real Estate families in SF are able to have an oversized impact on electoral politics in the city.