I think there is a real problem here (basically: "saving is not fast enough"), but I don't think the proposed solution ("skip the save dialog") is a good one.

Wikipedians often feel very strongly about using edit summaries and I worry that a vocal group would be very mad at us if we made it too easy to skip them. (And as a Wikipedian, I would agree with them, except I wouldn't be mad. :) ) Additionally, this would presumably require a preference or something, which has a maintenance burden.

But there may be different ways to make saving faster and more convenient…

One that immediately came to mind is using keyboard shortcuts, which we already support – on desktop, you can press Alt+Shift+S (or Alt+S, depending on the browser) and then Ctrl+Enter to save your edit in about 2 seconds :) (Ctrl+Enter is a generic shortcut that works in all dialogs). But I'll admit that this is a bit of finger gymnastics, and perhaps not exposed/documented well enough.