Eh, the issue with rushing 
is that it's damage scales with HP, so building it first actually means it is not doing much damage at all. In other words you get significantly more benefit from Tri or cleaver in early stats+damage+their passives in general (movement+armor shread / sheen+movement) .
Also wave management is very important early and having something that constantly pushes takes wave management slightly out of your control (you're forcing to shove than to freeze)
If you want to rush a tiamet item, 
is significantly better since it offers sustain for better trades, and more raw damage.
As for champions themselves, the item doesn't work well with them because there are simply so many better options. 
benefit massively from the cleaver rush shredding armor (making their abilities and autos do more rather than just tiamet autos and active) and it helps them stick to their target better.
on 
is just way too good since they do on-hit damage with some of their abilities ( sheen, which is a huge powerspike, buffs their ability damage and their autos in between their other abilities).
I can't speak for because they're not even meta to begin with
from what I seen never builds a tiamet item regularly but one of my diamond one trick yorick friends doesn't infact build over after trinity.
Overall, titanic is a good item mid game when you have the HP to back it up, wave management becomes less important and you're trying to get moving or splitpush, but if you're doing a tiamet rush build on anything, ravenous all the way for the lifesteal, or just sit on the tiamet until you finish your first item, then upgrade the tiamet into a titanic (what Warwicks do).
but titanic seems to be a way better first item for the laning phase with its high damage. I need to do more testing to confirm this though.
