Two reasons:
1. Evaluating people by "solved problems" encourages them to solve problems rather than do other kinds of work - which is often more important.
2. You can't evaluate people by their real performance - only their perceived performance. You're splitting them up individually to do so as well. As you are a human being, your perception is biased and your information is incomplete - there are many, many people who would take advantage of that to make their work seem more important/better. Hence, self-aggrandizing.
If you want people to do their best, give them the power to do self-evaluation and ask them to find ways to improve their work/their team's work.
If you want to fire people, your absolute worst employees - the bad ones who somehow survive layoffs, are the ones who are going to abuse your perceptions and metrics the most. The only way to get around this is to gather metrics in ways that can't be self-reported or influenced by the individual being evaluated, even indirectly, except by being competent at their job.
If you want people to do their best, give them the power to do self-evaluation and ask them to find ways to improve their work/their team's work.
If you want to fire people, your absolute worst employees - the bad ones who somehow survive layoffs, are the ones who are going to abuse your perceptions and metrics the most. The only way to get around this is to gather metrics in ways that can't be self-reported or influenced by the individual being evaluated, even indirectly, except by being competent at their job.