So the problem with
as a core item is 2 fold.
1, you have a very wavy power curve and Jarvan really kind of wants to be fighting all the time. Building dominik's is more a spur of the moment "Oh I have 3k gold randomly, Ok, lets buy THIS" kind of item. (I thing I have most CERTAINLY done to hilarious results)
however, then there's the second problem.
It doesn't have any cdr and none of the items that go with it do either. If you build dominik's you really want to then build a last whisper and a blood thirster to get the maximum possible effect out of the passive. But then there's ALSO the problem that you need to actually play like an assassin and sit back and never auto attack a tank unless you mean to kill them.
Trinity doesn't have ANY of those problems and it was always an ALMOST good buy on Jarvan but it always left me with a "Well, what the hell do I buy now" kind of feeling. The passive aa proc was good and the attack speed was... meh, the crit I would rather not have at all because Jarvan's Crit animations are fucking dumb looking, almost like they're telling you "DON'T GET CRIT WITH THIS GUY" and the move speed on unit kill was on the black cleaver which I would rather have instead to be perfectly honest.
But an extra 25% attack damage is a turret that I can kill 25% faster. And damage Jarvan already kills turrets surprisingly fast. Like he can give Yi a run for his money, add a tri force proc to that and holy shit, now I know what I want to do, I want to go fast! 20% cdr is so fucking good too it's unreal, and if I just buy a black cleaver AS WELL well now I have 40. And this hydra is giving me sustain after I solo someone and hey shit, I'm a really really good split pusher who isn't completely useless in team fights because of my flag and my ulti. NOW I know what I am!
I'm BULLSHIT!