I hire at a FAANG for two roles where we specifically target generalists: Solutions Architect (design solutions for complex real-world problems) and Technical Solutions Engineer (last line of support for really gnarly cases). Both need people who can cover a lot of ground, and it's hard to be good at either if you don't have significant practical experience and can't traverse the stack from source code to tcpdumps if needed. That said, being just a generalist is not going to cut the mustard, you're going to need depth in at least one field, plus you need to be able to talk to customers too.

Mandatory plug: if you think you'd fit the bill and are keen to explore, find me through my HN profile. Bonus points for being anywhere in APAC, although I can refer you elsewhere too.