What exactly is the problem with with being a rift mage that uses lightning spells?

You mean debuff effects? Meh, not a great loss. I was worried that it decreased damage or something.

I didn't know there was a problem, that's a new one on me. So where does it say that exactly? I must admit I tend to prefer Knight Enchanter as my specialism but I have used Rift Mage and I don't recall having lightning spells impacting on it.

It's not really an explicit thing, it's just an unfortunate and not-well-thought-out side-effect of a certain spell combination (which are not super-well documented in general, in-game). Basically, Shock (side effect of electric damage) + Weaken on the same enemy puts the enemy to sleep, which would be good (and can even set up combos to be detonated), except it also removes both statuses. Since Rift makes heavy use of that mana regen ability, and since it can combo off itself anyway (Winter's Grasp or Ice Mine + Stonefist is actually even easier in fact), it's just more of a drag on the build than an advantage.