I think most interviews are designed to find people similar to the interviewers, whether they realise it or not. If you think it works "well enough", I think you're just fooling yourself.
I say that as someone who has gotten a job offer from every interview I've been interviewed, and done maybe 100 on the interviewer side of the table. I put far more weight onto pair programming and anything that resembles a work sample than anything else. And even then you don't really find out what people are like until like the tenth pull request or so.
Getting an offer from every interview is impressive, good for you (you don't cite how many but I'm assuming you've done a good number in different contexts). Even the smartest people I've known have had mixed luck with interviews, due to some combination of randomness, poor interview design, or just poor fit for that company. As for administrating 100 interviews, you'd prob rack those up in a 2 year stint at a FAANG (usually they'd start you around 6 months in or earlier and you'd do 1-2 per week thereafter).
Anyway, yes, interviews are prone to bias. So are work samples (in different ways). Pair programming can be better but logistically harder (i don't know any companies that have been able to do them at FAANG scale), but even then, like you said, you'd need a lot of it to really judge.
At the end of the day, the entire hiring process needs to work "well enough" and with reasonable cost to both company and candidates. For many FAANGs, these interviews (plus hiring committees, bar raisers, or something else) meet that criteria... Though honestly, they often fall short on diversity but that's a whole other topic.
I'm 40 (ouch!) and I've done about 6 serious interviews - other conversations over lunch and whatnot, that I didn't pursue - I'm not a serial interviewer, granted. Three job offers I declined.
Where I work today, I'm in the last round of interviews, to try and reduce the time consumption.
My real point is that a work sample is really hard to get in an interview, and it's really not fair to fire someone in their evaluation period because they're only average, and not extraordinary, with what they come up with in day to day work.
I say that as someone who has gotten a job offer from every interview I've been interviewed, and done maybe 100 on the interviewer side of the table. I put far more weight onto pair programming and anything that resembles a work sample than anything else. And even then you don't really find out what people are like until like the tenth pull request or so.