I asume the 'other juggernauts' you mean are darius, garen and sett.
Darius and Garen both have truedamage ults and %pen/shred in their kit, they don't need BC to deal with armor. They both also benefit from AS, darius for stacking the passive and garen for his E scaleing.
Set is pretty new, rather AA focused in comparsion and has plenty anti tank tools, and unlike others he doesn#t benefit much from the all physical damage speed proc cause he always needs to get into AA range first.
Illaoi Has not %pen or truedamage in her kit, hardly benefits from AS and has the worst backline acces amongst them, so getting the %pen is rather important for her. She also has alot high ranged physical damage that with BS procs the rage bonus MS that only works on AA with trinity.
I'm also not 100% sure on her E, it could be that it gets double mittigated by armor(first the damage to the vessle gets mittigated, then the transefered damage to the actual champ gets mittigated aswell) in which case arpen would be even more valuable.
That said, i think vs squishy setups, trinity would be steronger on Illaoi aswell, but usually you use her as a counter pick to frontline heavy comps. Squishy opponents tend to be high ranged or mobile, and illaoi struggle alot against that.