Let classes choose their OWN cross class skills (level sync woes)

[Felis]

Exactly , if you were to be able to use your own cross class skills, a white mage could slot Stoneskin in one of his first cross class slots and never lose access to it. Makes no sense, for every other class to be able to slot it and have access to it at early level while a synced white mage doesnt.

This goes for all abilities like that, swiftcast etc

It is because only the current class (in your example the CNJ/WHM) get level-synched, while every other classes on the character not. So, you can't use it because the CNJ don't have the level for it. If you are on another class, your CNJ would have the level and you can use the skill on the other class.