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Because, if you believe people can not evaluate their co-workers, then you must disagree with the above article."
The article includes that there are times when you can't evaluate your coworkers and don't realise that you can't, when it says: "giving someone the wrong “level” of compliment. For example, if they’re a very senior engineer and you say something like “PERSON did SIMPLE_ROUTINE_TASK really well!” — that doesn’t reflect well on them and feels condescending. This can happen if you don’t know the person’s position or don’t understand the expectations for their role.".
You might think you know their role and expectations of it, but they might disagree - and their manager might disagree. Your position seems to be "vote on people you know, once per time period", and the article's position seems to be "feedback on anyone who does good work, any time, with their permission"
Your system will lead to:
1. You know more about people you work closely with, than others.
2. From them, you will have opinions about who does good work.
3. When it comes to voting time, you are incentivised to put that aside and vote in a way that keeps you with people whose company you enjoy, not people who objectively contribute most to the company goals, as a manager would see it. Because you have a limited number of votes, and votes exist as a rating for promotions and firings.
4. Managers have no idea why some people were voted for, or whether the people voted on think it's a fair vote.
The article's system will lead to:
1. You see any piece of good work which catches your eye.
2. You approach the coworker and talk to them, when you might not otherwise have done so, ask permission and explain why you think it's worth feedback, building connections between employees.
3. Managers get smaller, more frequent, feedback with explanations and know that the coworker agrees with this judgement of their work. Managers know who sent the feedback and whether they trust your judgment.
4. While the people you feedback on are affected by it, it's nowhere near as direct as 1 vote -> your only influence on the result, so you can afford to be more generous and less self-interested.
Other differences between the article and your suggested approach: you are not limited to 3 votes when sending feedback, you can feedback on as many people as you like. If you send feedback as and when it happens, you're less affected by recency bias from the last few days before voting day. You aren't obligated to send any feedback, but you are obligated to vote for 3 people, even if you think you have only 1, or 5 good coworkers.