Kel'thuzad is the Patron Saint of All Necromancers, the title being only contested by Ner'zhul and Arthas themselves, so the fact that he didn't use his infamous phylactery to ressurect himself, instead telling Arthas that he needed to go all the fucking way to Isle of Quel'danas to ressurect him seems odd to me.
Sure, Kel'thuzad was powerful, yes, but not that powerful. He wasn't a Medivh for fuck's sake. Well, not at the time. (KEL'THUZAD'S SECOND DEATH IS ALSO A SETBACK, THAT MOTHERFUCKER IS JUST TOO FUCKING AWESOME AND CRAFTY TO DIE) Perhaps he sought to increase his own considerable power via the Sunwell, or defiling it was the primary goal in the eyes of the Lich King, and Kel'thuzad's increased power & return to the ranks of the damned was actually a side bonus, or Kel'thuzad wasn't meant to survive, yet came back due to having manipulated Arthas to ressurect him with Sunwell's power.
I love the headcanon of Kel'thuzad pulling a subtle fast one on Arthas and Ner'zhul re-evaluating his lieutenant and thinking "Well played, you magnificent son of a bitch."