Full-screen "loading" overlay in desktop browsers

We've recently introduced a full-screen modal for loading operations in our web app to provide better UX for small screens. The problem was that the loading spinner we had before was sometimes out of screen on small screens.

Our solution just displays a semi-transparent overlay with a spinner in it for operations that take a moment for the server to process it - usually this is fast, but on slower connections it can take a few seconds. I think the overlay provides a good UX on mobile devices.

We now tried to use the same overlay for large screens, too. While some of our team members like it, others think that it is very distracting. Especially when server-side operations complete quickly, the semi-transparent modal appears in just a quick flash, leaving the user wondering what just happened.

Are there any best practices or guidelines about full-screen "loading" overlays in web applications? Are they good, or should they be avoided?

Note that the quick flash can happen on mobile devices too, but there it is less distracting because the screen is smaller and users are more used to full-screen loading modals on such devices.