We kinda just did away with a system like that - before SB we had cross class skills, that required you to level certain classes to get them.
For example Swiftcast was a level 26 THM/BLM-skill - so every BLM would just have that skill as part of their native tool-set, while any other caster-class could take it as cross-role, given they had THM leveled to 26.
It was, quite frankly, annoying. It forced people to level jobs they had no intrest in leveling. We're even getting kinda rid of it now for the crafting-classes because for the longest time you had to basically level all of them to max-level to be able to actually make endgame-gear (now they're all getting the same skills and especially skills that can replace the 1-60-class-specific ones) Please dont bring that back...

Why does there need to be a "reward" to level other classes? Why does it has to grant you and advantge when the real advantge of the game is that you can level as many classes as you wish. If you want to only play BLM - you can. If you want to level everything - you can do that aswell.
Unless we're talking cosmetics here for the LB, I really want to say "No, thanks" to this idea.
I dont wanna have to level monk to almost max-level again to get that healing-buff for my bard. I know enough healers who were unhappy about having to touch BLM at all to get swiftcast. Having to get GLD up to get provoke was a pain - specially when you met warriors in tank-swap fights who hadnt done it. And they shouldnt have to! We enjoy the freedom of playing whatever class we like now - dont change that to "Play whatever you like, but to be really effective at it you also need to level this, this and this - have fun playing melee!"

And besides that: A lot of skills work within and for their respective class. Foul depends on BLM-specific mechanis. Bards have skills that are connected to their dots. SMNs toolset is all about aetherflow-managment. Any skill you'd give to another class would be a cheap rip-off and the effect wouldnt be that you'd feel you're being "rewarded" to have leveled that other class but in most cases that you're obligated to do so.

If there isnt a great difference between the LB and "your Foul" that really sounds like only a new LB-skin... which I'd file under "eh, nice to have one day, maybe, but not the slightest bit important or even intresting for me"

(If you want to change the LB I'd consider it far more useful and intresting to make it not job-bound but to have everyone pick what LB they want at the start of a fight. Cant be changed during, just like cross-roles, but everyone would have free choice between caster, ranged, melee, tank and heal LB - I wouldnt mind throwing in a few extra "special" ones that could pick, something like the DPS-Lb being 75% weaker than the standard one but inflicting a 10 sec vul-debuff on the target. Or a combinde tank-heal-LB that grantes only 50% of the damage-protection we're getting now but a 10 second shield and a 20 second regen on top of that)