Karthus should be able to cast Q while moving

Are you serious? Syndra's q doesn't have less than 1 sec of cooldown and karthus's q deals more damage than syndra's if the other champ passes through his gate. There is no reason he should be able to cast it while moving.

It's not just about chasing potential. Karthus has enough chasing potential right now anyway, land the gate once and you shouldnt need it again until the guy is dead.

The real problem with this would be that chasing him would become worst than chasing singed. You know how hard these Qs hit? And as I said, his cooldown is lower than 1 sec on it. One of his important weakness is the fact that he can't escape, he either has to fight where he is or try to run without landing damage. If you give him that, he will become op, i guarantee it.

Giving Karthus more chasing than he already has as well as kiting/dodging skill shot while attacking is gonna make him go over the top.