No system is perfect.
If the residents pick, it could lead to a popularity contest. It can lead to the popular clique getting their person in--reinforcing their own groupthink position.
If the faculty picks, it could leave out resident opinions that are valid. The faculty might want someone that'll just satisfy their ends without acting as a person who can bring up the concerns of the residents.
If the PD picks, if that PD has poor insight into his/her program, or that PD is not a good judge, then he/she might not pick the best person.
No matter what system is used, there will be years where it does not pick the best person. I can tell you from personal experience, during my 4 years, any of the above systems would've picked a bad person depending on the year (well maybe the latter wouldn't have--we had a great PD, though I've seen several programs that didn't have a good PD).
It is something that I too would be upset about. A bad chief can a make a year go worse and its a title that can open several doors for the chief, so someone not right for the job can be getting an undeserved honor. My chief my PGY I year blew, and I got plenty of horror stories with her that were a result of her not doing her job right. In her defense she just delivered a kid and really didn't seem to care about being chief--so why then did the program pick her? She was the only PGY IV that year at my location. All the better ones left to do child psyche.
If you're not happy with the pick, only thing I can think of is talk to the PD about it. However doing so may not be wise. In several programs the PD is not open to hearing complaints without it costing that resident to some degree.