What would be your reasoning behind felons not being permitted within law enforcement?
Also, many felons are hesitant to put others in the same place/position they were once in. It presents a great conflict of interest. Also, just because you have served your time does not mean that you should be eligible for every job available.
Quite simply - it's an officer's duty to uphold the law...a felon has already proven he/she doesn't respect that.
Similar to Ichi...why would we choose someone who doesn't follow the law themselves, to enforce it?