I've rarely seen a time where a level up reward had only off-class abiilities, usually at least one maches the class. Good to hear that was intentional and not just my RNG luck at play. That said, i also like this idea as an option. But I think I'd want something slightly different from what's being suggested.
From the sound of it, you currently weight the probability of all ability rewards from level ups and lore chests. What if "no cross-class abilities" was applied only to level up rewards, and the lore chests got their weighting removed to compensate? You'd still get a random mix of abilities on a run, but your level ups would be consistent and reliable class-specific skills, while lore chests would be MORE likely to give off-role abilities.