I would be willing to bet that 95% of native English speakers can't confidently define "first cousin once removed" (though most of them will have heard the term).

Except it doesn't! In fact, first cousin once removed(FCOR) can mean both: your parent's sibling's grandchild, OR your grandparent's sibling's child. These are usually two very different relationships(if they exist) - the former FCOR is usually much younger than you, like a niece/nephew, and the latter FCOR is usually much older than you, and more like an aunt/uncle

I wager most native English speakers understand the concept of cousin, but not first/second/etc cousins, nor once/twice/etc removed.