I've seen FAANG engineers apply for engineering roles outside of "big tech" over the last two years (owing to the layoffs.) And, at least as it comes to "old economy" clients (like banks, financial services, airlines, etc.), agencies, and consultancies, the skill-gap is huge for the money and seniority that is desired. Likely, this is all true for start-ups.
I believe the skill pathways diverge too quickly — at a certain seniority or specialisation it's very difficult to move laterally between FAANG and non-FAANG organisations. Where as mobility within FAANG or within non-FAANG organisations remains high (job vacancies permitting.)
This contrasts profoundly with the job requirements posted by your run-of-the-mill recruiter, who looks for years and years of specialization on specific tech stacks.
My experience in one of the FANGs is the exact opposite: they value jack-of-all-trades that can onboard onto a new project at the drop of a hat and hit the ground running, regardless of prior experience. Their goal is to have organizations where engineers are perfectly interchangeable and replaceable if need be, which is key to fire whole teams without having any relevant impact on productivity.
It's recruiters who post impossible requirements regarding professional experience on specific combinations of tech stacks, which culminate in the old meme about job adverts requiring double-digit work experience in brand new tech stacks.