if a fund and its followers are all offering illiquid brkb calls

I'm not sure why you find them so illiquid?
It's the bid/ask that matters, and for big traders the depth at that bid, not the trading volume.

I find Berkshire options pretty easy to trade even in pretty large quantities, and the gaps are pretty narrow for the strikes that are somewhat near the money where one would likely be writing calls.

As a random example, the March $370 calls have a bid/ask gap of 25 cents these days. (it's a call I wrote)
You could probably sell those for 5 or 10 cents above the bid using a limit, which is only 2.5 to 7.5 cents off the midpoint, or 0.01% to 0.02% of the stock price.
Even hitting the bid 12.5 cents below the midpoint, that's a gap loss of only 0.04% of the stock price.

These aren't obscure small-cap options where the bid moves away from you when you get anywhere near it. You can probably hit the bid all day if you like.

Whether writing Berkshire calls is a worthwhile way to make a buck is an entirely different question.
But I don't see any insurmountable problem in terms of market depth unless maybe if you're trading well over a hundred million worth of notional value in a day.

Jim