Maybe it would expose you to information that's outside your own personal experience?
AT&T was quite a big company in its prime, a monopoly in fact, but extremely innovative. Same goes for Xerox. I suspect Google's longer-reaching research efforts (quantum computing, machine learning) could pay off similar dividends eventually, if they aren't regulated out of existence.
Yes, big companies are often hampered by bureaucracy. Many are not innovative. And in all cases, the majority of employees need to focus on the bread-and-butter work that keeps the lights on. But big companies also have the resources needed to invest in long-term R&D with potentially big payoff down the road.
Conversely, you could make the case that most SV start-ups are actually not that innovative, and that SV as a whole gets perversely fixated on the past: every occasional success, whether it's social media or mobile apps or the gig economy, spawns a thousand imitators hoping to cash in on past success. Do we really need to be funneling hundreds of billions of dollars to create more "Like X but for Y" smartphone apps?