Lets get this out of the way first: Yes, you should just clean up the messes on your stove top before they dry and cook and turn into greasy mystery gunk of unknown vintage. Of course you should do that. But you don’t. Or at least I don’t. Not every time.
I had tried virtually everything to remove the little cooked on spots around the edges of my stove burners, and everything seemed to help a little, but nothing really worked well.