I don't think it's necessary to exhale all the time while changing the mask.
Suppose you have to do a safety stop and the (main) mask has broken.
And suppose you still want to have good underwater vision during the stop: you can imagine that it would be useful to have a spare, but for a similar purpose, where we are close to the ascent and therefore there is no need to equalize the mask, you could even have simple goggles with you, as a backup. They are less cumbersome than a mask and many models are foldable. You can empty them with a maneuver that does not use air from the nose, but the air from the regulator, slightly raising the lower edge of goggles. I tried it myself and I managed to empty them enough from water to have good visibility.
This solves the problem of vision.
Now let's consider the problem (for those who consider it a problem) of water in the nose. Those who do not consider it a problem are not interested in the rest of the discussion.
Well, it is obvious that you just have to hold your nose with one hand, when needed or even all the time of the safety stop. Or if you want free hands (or don't have hands at all like some physically impaired divers), just use some device that keeps your nose closed for the necessary time. Basically, I don't see any big problems in managing a break of a few or even many minutes, without the mask. In principle, if you don't have to use your hands (or other voluntary gestures) to isolate the airways from the water, you could even think about taking an underwater nap