I think a lot of the relationship between an archer and a coach is based in how they work together as people. I don't mean that they have to be friends, but that their basic approaches and attitudes have to match up to a certain degree and - particularly importantly - their teaching and learning styles have to fit together.
That said, most counties/clubs are short enough of coaches that there isn't a great deal of choice in who one works with, either as an archer or a coach. I've done a teacher training course, although I never got as far as teaching, and the knowledge I use most from that when I'm teaching or coaching archers is centred around different methods of teaching and learning. I don't know whether any of this is included in current
GNAS coach training, but if not it might be worth considering. Without it, it can sometimes be difficult to realise that someone's failed to grasp what they're being taught (c.f. geoffretired's point above about getting students/archers to 'talk back').
Personally, I think the new coaching system has a lot to recommend it. Anything involving standardisation and centralisation is inevitably going to cause difficulties and mixed opinions in the beginning, just because it's changing an extablished pattern, but that doesn't mean it's not a better system long-term. I think that most things which help make archery more visible, or more easily understandable by the general public are a good idea, and having coaching levels which can be easily compared with those of other sports can assist in that.
That said, we all know that a piece of paper doesn't make a good coach. I think the key to any system of qualifications is in the quality of the assessment; if that sets a high and consistent standard, the qualifications will be respected. Unfortunately, high and consistent standards often mean monitoring, which can mean paperwork, accountability and 'tick-box' curricula, most of which are inherently unpopular.
Looking back at this, it doesn't really contain any answers. I suppose I'm musing on the theme - apologies to anyone who feels I've taken up too much space doing so
. One final thing - personally, I think a coach is an essential part of performance; I'd be lost without mine.