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.