Not a Google-specifc problem, I know people who have left several other big tech companies for "too hard to get a promotion" reasons.
Also worth noting: at massive companies, the part of the company you work on can make a big difference. Even if the processes are the same as documented, they'll differ in practice.
I really, really don't like perverse incentives that lead to things like "promotion driven development".
The alternative is job hopping for promotions, which is a drain on institutional knowledge.
At the same time, "whether or not your manager likes you" is also a shitty way to decide if someone gets promoted, because bias, deliberate or not.