After you get corprus disease and the wizard Divayth Fyr permanently
cures your bad symptoms, you still retain the good effect of never
being able to get corprus again (because you’ve still got it).

But does having (symptomless) corprus also have the effect of never
being able to get common disease or blight disease again? Should I
sell all my potions of Cure Common Disease and Cure Blight Disease?

Yup, your disease resistance have been increased to 100%, which means you’ll
also be immune to vampire bites (which is implemented as a disease), unless
you lower your resistance intentionally with potions.

That’s not entirely true. If you have the Bloodmoon expansion your
character will contract lycanthropy – no way to avoid it if you’re
playing the story line quests. It’s curable with a cure common disease
potion.

On top of that, even though my PC was the Nevararine and had 100%
immunity to all diseases, she still contracted a disease called Ataxia
from the plague bears. I suppose that the immunity to common diseases
only applies to diseases that are common on Vvardenfell.