Are you serious? One-off-ability came from the Frame?
Nah, One-off ability is not Frame specific.
Trust me, the frame is mostly useless without the core.
The core provide Energy barrier, Absolute Barrier, power source, One-off ability/Unique special ability. self-evolving ability, gravity-manipulation....etc
In short, the core make IS an Infinite Stratos instead of a bulky suit thingy that can't even work.... An IS without the core is basically useless.....
Edit: Only Byakushiki's and Akatsubaki's core can have unique ability because Tabane spent the most time on them.... For other cores, you have to blame the world governments for pushing her to create more and more.
Using Gundam term: Both Byakushiki's and Akatsubaki's core are super custom Prototype.
while Other IS' core are just mass-production grunts...
Yea....life is really that unfair in IS-verse.