Years ago, I thought, "Why would I want to bust my butt to join Goog or similar and be a cog in a giant machine?" It seemed to me like you try hard to prove yourself to get in just to be on the bottom of the totem pole where being recognized would be very hard. So I didn't bother and worked at other smaller companies.
In retrospect, it seems like your best move in the Valley IS to just try to get in to the biggest, best name, with the most talent flowing into it. IF and when you want to leave for somewhere smaller (or start your own), you'll be well served for having done it, networked, gotten the resume boost, etc.
So while yes, it may be true that the updraft opens up spots, maybe if you get one, you'll be looking back and seeing that during those years, having Goog or similar on the resume will not be as boosting to your career as Uber or AirBNB et al.
even better to get into such a company before it becomes that "best name". Unfortunately, on couple occasions i wasn't able to recognize it - they were such ugly ducklings back at the time :)
Is recognition one's main objective when working at such companies?
Some people do it for the pride. But for many the chance to work on some great projects and learn from arguably the best in the industry is an opportunity which is too hard to pass up.
Just like good people flocking to a company don't necessarily diminish the company's appetite for hiring lesser skilled people, it might even make hiring `minions' for the `rockstars' more attractive, if they are complementary.