I imagine there would be potential problems due to the fact that people have differing opinions about what people deserve.
For one thing, there are different but equally reasonable criteria on which to base "deserve." Maybe Bob in Engineering contributes more to company profits than Steve in janitorial, so Bob deserves to get paid more. Or maybe Steve is intensely loyal and stuck with the company through hard times and often stays late to get everything done, so Steve deserves to get paid more. Or Joe in sales hasn't been selling well this year, but his kid has cancer and he's obviously distracted and he deserves high pay because he's having such a hard time.
And of course, given a choice of criteria, people will invariably tend to choose whichever one gives them the results they like. Bob will be more likely to think the profit-based evaluation is best. Someone who's good friends with Steve will think that loyalty is more important.
Maybe it can be made to work (and it definitely can work in a smaller company), but I don't think it's as easy as you make it sound. Sometimes it's just impossible to please everybody, and if you try then you'll only succeed in displeasing everybody.