I've always done those quick checks myself because otherwise I'm prone to making errors. They give me a quick answer of "no, you can't do this" but I never found they actually improved my understanding of anything. It just told me I can't do the thing I wanted to do and it was time to move to the next idea. It's a valid proof, but not one that really ever helped me get a grasp on what's happening.

Mostly it just means I'm in trouble and need to be really careful and do more checks because I'm working with things I don't understand fully.

For example, I've never needed to do that sort of check with adding fractions. I have enough understanding of what those numbers represent and how they work together that I've just never thought I might want to add numerators and denominators separately.