Why do you have to play at a high level? How many coaches were AHL players? How many GMs played at the NHL level? How did Gretzky's coaching career go? Evaluating talent and playing the game are two completely different things. You sound like Kevin Lowe I have 4 rings I must be a great GM.
Those who played at a high level are far better at evaluating talent for the most part, because those of us who didn't don't even know what we're looking for. You can watch a lot of hockey and still not know how to look for the small things that make the difference for players - and most people who watch a lot of hockey fall into that.
Among current NHL head coaches, I believe 5 never played AHL level, but 3 of those played university level hockey. According to Wikipedia, there are only two without playing hockey at a high level - Andre Tourigny from Ottawa (he didn't have anything other than coaching career listed), and Jon Cooper for Tampa Bay, but even he had high school hockey experience and played university level lacrosse, so he was a pretty high level athlete as well.
Meeting your "AHL or higher" standards, 11 didn't make the cut, BUT, one of those played ECHL with a cup of coffee in the AHL (Treliving), one played junior hockey and was a junior hockey team owner for years (McKrimmon), two played University level hockey, and one grew up with one of the greatest hockey minds ever as his dad (Bowman), so none of those are comparable to the common hockey fan analyst. That leaves us with six, two have backgrounds in law, and one moved through the ranks as a scout, so I don't think those are comparable either.
Gretzky having a poor coaching career isn't relevant here. One former player being a bad coach doesn't in any way mean that having high level playing experience isn't important for coaches, it means that some players aren't built to be coaches.
Evaluating the talent and playing the game are different, but not completely different. There is a reason that most scouts, coaches and managers in pro sports are former players. Not only do they understand more about the game, they have lived it. That's why most experts are former players, and not stats guys who can break down numbers.
As per the Lowe thing, it isn't relatable here either. He was saying that he knows about winning (and in one sense, he obviously does, even if he was wrong in that his playing career success automatically made him a good manager). That doesn't mean that saying that most players and former players know better than fans is incorrect. If fans knew better, we wouldn't see fans wrong so much of the time. Even smart fans like those on HF.