Imagine you talk to your manager and coworkers regularly to get feedback but you don't put the negative feedback into a formal software system that encourages politics and backstabbing!
You're right though that the feedback should not be anonymous, I've seen that in action and it just leads to the kind of Machiavellian scheming you describe.
But if (non-anonymous) colleague writes in a system that she thought I was brusque to her, that I wasn't communicative enough during a project, I'd rather know immediately so we can talk it out rather than have her lob it like a bomb at the end of the year.
So if a colleague writes an email to your manager, your managers manager, HR, and to your future manager about your poor handling of an issue you would take that well?
Better than to an email addressed just to you?
The point of this system is to get that feedback immediately instead of down the road.
You want to junk review systems completely, OK. But if you're going to have a review system, better to get that info in the moment.
I'd also add that negative feedback of others makes you (the complainer) also look bad, so there's a built-in incentive for career-minded people to be judicious in their response.
I'd argue it has the potential to make it better since it creates a papertrail and transparency. I'd rather that than Joe Angry Developer sneakily badmouthing me to my boss or my co-workers behind my back.
Worst case it seems like a lateral move as far as politics goes.
How would you respond if I file a HR complaint about you or send a complaint to your manager?
Better than if we had just had a quiet word?
Or now rather than blowing off steam by complaining to another colleague that e.g. you don't want to delegate your co-worker will formally report it into a system used to manage compensation and career progression.
Others will game the system and make sure people write lots of positive comments about them. Now when it comes to the next pay cycle I have dozens of positive comments and you have a couple of positives and a few negatives. Guess how that will work out for you?
It encourages people to complain in the heat of the moment.
Etc etc etc.
Not to mention that people who want to badmouth you behind your back still will.
These things only matter when you need to justify a raise or cover your ass for a termination.
To stretch your analogy... if your spouse doesn't tell you they hate your cooking, that's the real problem: trust and communication. Asking them for feedback after every meal won't help resolve the real problem.
But often, it's not.
A lot of colleagues and managers are too timid to provide timely feedback, they think they need a formal moment like an annual review to speak up.
Do you believe every single employee and manager has the skillset you describe to be open, honest and trustworthy? If not, then having a system to help shepherd feedback isn't a bad idea.
If the critique is fair, timely feedback also gives you a chance to change instead of letting it build up until they hate you. Imagine your wife/husband told you they always hated your cooking. Why not tell me before instead of while we're divorcing?
If you're guaranteed to get feedback, it's always better delivered in a timely fashion.