Here is an easier way to fix it all:
Let certain earned abilities, like the PUG ability to get an extra 10% from healing spells, simply become passive on your character no matter what job you equip. You have 5000 hp... you get healed by a cure III for 500... you get an extra 50 hp... a small amount. * numbers here are all adjustable ( in practice you would probably change the skill to an extra 2% when not PUG-based main job).
It's like a merit system, you still get a small reward for having played and leveled other classes. I think everyone wants to be a better adventurer for having spent the time to level another class. Another example... the CON Fast Cast... once you learn the ability, all your magic spells will cast at an extra 2% faster regardless of what class/job you chose, and 5% faster on any CON-based class you chose.
These passives would be active after earning them, and never erased from your character. So your level 1 ARC would start with a passive 2% fastcast and passive 5% healing recieved, because your CON and PUG had already been leveled up.
This isn't a radical overhaul, it's just taking existing bonuses, and making them a part of your base character. Like merits from FFXI. It rewards players for having leveled a different class, fits into the lore, and removes the need for 'class afinity' that creates 'grey mages' that have access to any spell they like, while still allowing for balance.
EDIT: This is not for ALL ABILITIES, but perhaps one or 2 per class upon reaching rank 40 or 50.
For example: I have reached CON 50 and purchased the 'Fast Cast' ability with marks. From now on, any job I play will have a latent bonus of 2% faster cast time and 4% faster with CON-related jobs (BLM or WHM). That is the ONLY bonus I receive for having a CON 50. It reflects the time I spent leveling CON, and lets me utilize my CON knowledge on other classes, whilst my affinity with CON spells is reduced to 50%.