Hard disagree.
At Google, in most orgs, manager can influence the chance of success significantly:
- Making sure their team works on what the org leads find "impactful"
- Facilitating cross team collaborations, which will lead to good peer reviews for your report
- Helping your report write the promo packet
- Presenting the promo case effectively during the calibration meeting and being prepared to advocate for the report and respond to criticism from other managers at the meeting
- etc.
There are many managers that do very few if any of these things, and it shows.
Yes, there are quotas, but nonetheless the manager plays a big role in whether their report makes the cut.
There is no harm in saying that you are quitting because you do not feel valued / rewarded enough. Hopefully it will effect change in the manager. Of course it's best to keep it polite and not burn any bridges in the process.