Why is illumi after alluka? Why is Illumi after Alluka's power? Does it have something much more powerful than just creation n destruction.
Alluka's power can grant any wish.
In return, Alluka will request (After granting said wish) 3 requests, with their difficulties adjusted to how complicated/strong the wish is. (Not sure how to word this)

If three requests are granted, you may wish again. If three requests are denied, people die. The number of people increases as I've said before. The people who die, die by order of closeness to the target. (Minimum 2 people)

Thus, if they were to harness Alluka's power, it would be mindboggingly useful, and would make the Zoldick family as strong as they can only imagine.
But if someone were to abuse it and fail the requests, the results would be devastating for them. (And Illuka believed that Killua wanted to bear the requests of his wish)

Illumi also believed there are rules they are unaware of, and only Killua knows of, and again, he is correct, and this would make anticipating and controlling Alluka much harder. Thus, he intended to destroy her.