Sort of..... I would agree that playing at a high level would necessarily give someone exposure to connections to get considered for "upper tier" coaching positions... regardless of whether they have a clue how to teach. (Beyond a certain point you simply cannot get into that club without the secret handshake) Just because they had the skills to play at a high level does not mean that they can teach those same skills to others. I have seen way too many former high level players that completely fail as teachers - all their lives that just did it, they never really thought about how they did it. SPECIFICALLY AS SKATING COACHES..... if you ask them to break down the stride, weight transfer and edge control, how to do it, as well as what game situations certain edge techniques might be good and well.... yeah - no bueno..... Yes a lot of kids are visual learners, but you still need to know how to break down their technique to fix the bad habits and poor technique that they ingrained through all of their "visual learning"..... having played at a high level does noting to instill this in someone. It depends on their personality, how they were taught, and even to some extent whether they were naturally gifted or had to work on it to get a good stride.
We do agree that to teach skating you DO need to be able to demonstrate the technique - THAT does not require that you have played at a high level.... Just that you have good technique. I think that you would agree that here is sooo much more to teaching skating and especially power skating techniques than just demonstration.
Go watch a coach teach.... you should be able to determine if they are any good and whether their way of communicating meshes with how your kid learns.