Hey, YOU came here and posted this here. YOU put it out there. Live with the scrutiny that's comes with it. Part of being humble and learning is being able to say "this is what happened, this is what I did. What could I have done better?" You're the one trying to justify why reluctance to declare an emergency is good. In this case, light area traffic. "More of you would've made that decision"......are you sure?
Fly the aircraft first, thats fine. But with two of you in the aircraft, planning a bit ahead and being able to communicate an emergency shouldn't have tasked you too much......since you practice single-engine on every lesson and all.
You knew the fire was out? Might I ask how you knew it wouldn't or couldn't restart post landing? Great that you found out after landing that it was nothing, but at the time in the air, you didn't know differently, or I doubt you would've shut down the engine in the first place. So obviously you thought there was something more than just the "after fire" going on.
If the pattern or airport is slow, what difference does it make.....I'm speaking generally for what pilots should do vis-a-vis declaring an emergency or otherwise being reluctant to. AND talking how pilots can help with ARFFs response time. It costs nothing for us to be there, awaiting your arrival. But with no emergency declaration you still waste precious time post-landing if something happens, such as the fire restarting, and now there's a ground emergency that's going to take time for ARFF to respond to, when they could've already been in-place.......and it would've cost nothing.
But you should already know that, being former ARFF.
Just all things to think about, in the learning processes post-emergency. Theres always learning to be had.
To answer your last question regards the FAA. I doubt anything will happen.