When the FSF says a license is GPL-compatible, what they mean is, "You can legally combine software under this license with software under the GPL to produce a new combined product, provided that new product is distributed under the GPL."

Assuming that FreeBSD's maintainers want to keep their code under the BSD license, they'll be wanting something more permissive than the FSF's "heads I win tails you lose" version of compatibility.

Yes; but if they want to release the BSD kernel as a whole under the FreeBSD license, then they already cannot incorporate code that has any other license whatsoever. For example, they wouldn't accept my patch under the hypothetical license "you can do whatever you want with this code except shoot bunnies". If they did, FreeBSD users couldn't use FreeBSD to shoot bunnies.

Am I missing something about the BSD kernel licensing social dynamic?

It's not about patches. FreeBSD drivers generally shouldn't be patches; they should be loadable modules so you can use them without recompiling the kernel.

Now if you changed your hypothetical so that it's not a patch but a separate module that compiles to its own distinct binary, and your hypothetical license were expanded to include a second clause, "Anything that links to binaries built from this code must inherit this license," then we'd be talking about a situation that replicates the issues with making use of GPL code in projects that use more permissive licenses.