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.)