I don't think it'd hurt anything, but I don't see the need either.
I think a lot of people used to do it for the reasons you previously did too. But I don't think that I know anyone who did it to a daily, or an almost daily driver. Just doesn't have the same need.
If you're losing prime in just a day or three then something else is wrong. Of course, that "something" could be the new fuels I suppose, in which case a primer pump might help.
As far as damage to the mechanical pump, I don't see anything that would hurt it any more than it would have in the old days of hunting and rock hounding rigs needing it after a winter's sleep or as a backup for when their primary pump failed.
That latter has some potential drawbacks (like leaking through a busted diaphragm) but I don't see the electric pump actually causing the damage.
But a lot has changed with the quality and capabilities of replacement parts over the last thirty years too. So there's that to contend with now.
Are you having trouble now? Or just thinking ahead in case it's a thing?
Paul