I personally don't see a point in having traits affect abilities that are not cross-classable. In this case, they may as well just make the ability like that by default.

For example, there could be a WHM trait for Cleric Stance that provides an accuracy buff. This accuracy buff would then only apply for WHM and not AST/SCH.

Physick, for ACN, could have a trait that in the 50's applies an INT based heal. Cure Potency: 400, INT Cure Potency: 100 or whatever, allowing for a bit more healing power while in Cleric Stance for SCH, or a bit more of a useful heal for SMN.