You do it by letting managers decide based on perceived performance, and trusting in their assessments. If the biggest factor is your direct manager in either system (which I agree with), we might as well stop pretending otherwise.

This has the same result as the formal review system, but with a lot less overhead. More importantly, if you're denied promotion out of spite, you know that - they can't just say "well, it's not my fault, it's just how the process worked out".

Yes, good managers can definitely help cut through the BS even with a process in place, it takes time and effort for them - time and effort that could be used on something more valuable. And sometimes, no amount of effort is sufficient to buck the process.

From my experience, by the way, a formal competitive review system (buckets etc) makes it more important to have a good manager, because you absolutely need your manager to play the game well against other managers to yield good results for you, no matter how hard you work. If your manager is indifferent, or can't play the game well, they'll take away whatever was left on the table after the rest, and that's what you'll be stuck with.