Now the objective measure itself might have some sort of bias, but at least the rules are set and you're not getting screwed over based on someone's feelings. You can argue metrics, you can't argue your managers feelings.
Replacing a subjective metric that's at least somewhat effective with a metric that's totally useless (because those inherent inaccuracies/biases are even worse than even a poor manager's judgement), that's throwing out the baby with the bathwater. The primary purpose of a performance metric is to measure performance, and being prejudice-resistant is something that's nice to have - the primary reason why you implement a metric is not because you need something that can be argued.
This shouldn't be surprise at performance review time, nor should it necessarily come from your manager -- it should be coming from your senior colleagues on each of your code reviews, giving you a chance to improve your bad code before it gets checked in. But when your senior colleagues think your PRs are worse on average than those of your peers, then yes absolutely you should get a worse rating.
You have to define productive engineer in order to claim the metrics are biased.
Or how about even if yours generates 10 comments on the PR correcting things to match code quality guidelines and mine doesn't?
I don't think we often track things like that.
I think it's impossible to create something like that and it'd be very very bureaucratic and still prone to gaming. I think having something 'in between' is the best approach. You still allow a manager to interpret these things together with you but the manager should give you a guideline for what to look out for. We can use these metrics to inform decisions about performance but it's completely counter productive to simply have a few metrics where you have to hit specific numbers.
PR throughput? No problem, I'll form a clique of a bunch of people that OK each others tiny PRs. This will result in so much overhead that we won't actually get much done, piss off other team members, create a hell of basically unusable commits, make it more likely that code quality suffers because nobody has any chance of having an overview of what you're doing overall and you will likely create regressions that developed over multiple commits and would've been caught otherwise because let's face it, each unit test you write is its own PR. You say obviously you won't get through with this because your manager is supposed to stop that? Well he can't if we just want a completely objective and metrics driven approach!
With the hybrid approach, you know from your manager that PR throughput is important not at the expense of quality and other things. You want small PRs for certain reasons but not at all costs. There is no exact formula because no two situations are exactly the same. Of course bias comes, of course bad managers make this bad. So does a completely "objective" metrics driven environment in which you play the metrics game. There is no perfect solution.
In reality I think someone who only looks at team members who are "doing the most" is really just measuring who is talking about their work the most. You need some kind of objective measures like features shipped, assigned bugs resolved, etc.
Also, the metrics you choose will undoubtedly contain a measure of your bias anyways.
For instance, the metrics two people would choose to represent developer effectiveness will not be the same, and those differences will reveal what kinds of workers they prefer.