I am curious as to why no one has played him as ADC.
People do occasionally play him as an ADC, but the massive disadvantage to doing that in Rift:
AA Range.
It's is really, really, really important to the ADC class. And Jayce only has 500 in his ranged form - which means essentially every ranged champion will out-range him and has the potential to pew-pew him to death where Jayce can't respond back.
This is pretty awful in the lanning phase for Jayce - as it makes it easier to punish him for CSing as any other marksman, and easy to poke and harass.
Also pretty awful in the team-fight phase: where range directly translates into a ton of safety by making a champion substantially harder to focus and much easier to protect.
And if you're playing him ADC rather than mana-gorged AD caster, his warp gate + shockblast combo is generally going to be to expensive to cover that weakness.
Alternatively - in Dominion and Treelines range isn't that helpful, as 150 more range just placed a melee capable of leaping 700 range at, like, 5% more risk. Jayce's mobility, self-peel, and melee-ranged pain make him a very powerful marksman in those maps where Jayce's particular strengths are considerably more valuable.
TLDR: only 500 AA Range.