Huh! I've always ironed mine in half, going to have to try it without the ironing. If nothing else, it saves a step that's a pain in the rear.
My bindings are often pretty sloppy, I just use the "galloping horse" rule to make them feel acceptable. They aren't TERRIBLE - they're structurally sound and I'm convinced that non-quilters don't notice anything amiss at all...but I think even a beginning quilter would notice some irregularities! I've improved a lot though, some of my earliest quilts have bindings that are pretty cringe-worthy, even by my low standards! (But they haven't come off after repeated washings, so that's something.)
In examining my grandmother's quilts, I think she had a similar attitude towards binding, LOL! She didn't even fuss with mitered corners; all her bindings are simply the backing brought over to the front and sewn down with boxy corner seams. I NEVER noticed or thought about it until I started making quilts myself.