If you could direct me to a source where the average fan, with an average amount of time, could properly research and scout possible head coaches I'd appreciate it. Because I don't know where it exists.
It's a far more complex and difficult process than you're implying. It's also something where I imagine an in-house interview is essential. You want to hear a coach's ideas and thoughts straight out of his mouth and we, as fans, just aren't going to get that.
This is one thing that I'm just going to leave to the people who are paid to do it. After a decision is made, I'll have a somewhat vague opinion but I'm always going to give the replacement a chance. Unless it's a Tortorella type situation, I find it unrealistic as fans to criticize something that is so complex and is done so much within the realm of people working professionally within the club.