Would angels need to be trained?
Think about it. I mean really give it a good think or two. Anything we do requires training of some sort, whether it is self-taught or learned from another. Most skills don't come naturally, which are why they are just that.
A new angel on his/her first day says, oh look out ma'am and helps a little old lady avoid a puddle only to step in front of a transport doing 60km/h. Oops. Bit of an accident on the job the first day could have dire consequences.
There'd have to be angels in charge of training, likely managers, supervisors, and well, it just becomes one gigantic bureaucratic mess. Though I highly doubt it would be a democracy.
Sometimes crazy thoughts happen in my brain...