I can agree that it's not so important for some games. Good old-fashioned button mashing (which I enjoy sometimes) and seeing an adventure through to an ending is fun pretty much regardless. Basically, though, I think that if the first point is to get better at a game, then the ultimate point is to 1CC it. I guess I'm drawing a line between action games that focus on skill and others that focus on...well, action.
The money-milking issue just makes things complicated. Let's not even talk about 2D fighters, either.
1CCing a good shmup is like playing a song all the way through without making more than one or two little mistakes, at most. A continue, though, is like a great big ugly mistake. Beating a shmup in MAME on your first try by continue-spamming is like playing random notes the whole way, or like playing each measure one at a time until you get it right and then moving on to the next one. I'm not going to tell you you can't do it, but that just ain't how the song is supposed to go.