Most champions normally do have things worth keeping in their kit, and his passive is certainly one of them, but yeah he does have a few problems.
For one, he's low range and likes getting up close, but unlike Swain or Vlad, he has zero survivability tools. This makes him heavily rely on items for durability, resulting in a behind Karthus being fodder, since he can't hide in a backline without losing half his damage.
His Ult, as cool as it may be, has some issues too. For one, you either use it before a fight, to pick up kills from other skirmishes or after you die. You can claim it's unique, but the power budget gets weird.
Since it's an Ult that can't be used at the drop of a stone, his basic abilities need to be good enough for his ult to not be 100% nessecary for the kill. At the same time, because it's situational, the Ult itself has huge power. Similar to Ryze, except Ryze's is pure Utility.
This can result in a fed Karthus spiraling harder when ahead, even more so with his high depedance on items. Overall, Karthus's kit is pretty legit, he suffers from a few design problems though. A Warwick level rework would likely be best all things considered.