The job abilities would have to *be* the pet summons and there would be all kinds of crap associated with having a class that goes from dealing all of its own damage, roughly equal to the other DPS classes, suddenly shifting a majority of its performance onto a pet. SMN and SCH are explicitly *designed* around having a pet to provide a healthy portion of their total damage: Ruin has a laughable potency of only 80 and that ends up being what a SMN spends most of its GCDs casting, since it's not like they have much reason to reapply their DoTs before they come up. The "loss" of the 6 attacks is completely negligible to the damage dealt, given the fact that they're not the foundation of the class; you're just having them lose a few mediocre utility powers. Plus, you're telling one job that it only gets 11 abilities, which is just handicapping the playstyle.
The only way you're going to get a class that "trades up" from a non-pet class to a pet class is if the *entire* previous DPS structure is revisited and rebalanced around the pet doing said damage: all of those attacks would need a separate potency for FLA/BLU and BST. The opposite is true in the same way: if you're getting rid of your pet, you better be getting some big buffs to make up for it.
You've still got all of the problems with your Blue Mage suffering from stat schizophrenia. You're claiming that they would be using magical and physical attacks, but they're only going to have the stats for one or the other (likely physical since, you know, it's a DoW class). It doesn't help that you're trying to blend in PIE and MND as well. Mechanically, you should just stick with a single stat. If you *really* want to have alternating Blue Magic and physical damage phases, just use an explicit mechanic that enforces it rather than trying to bend reality to accommodate stat schizophrenia: just have a stance called "Blue Magic" or something that swaps your STR for INT. Of course, you'd need to have some kind of mp regeneration mechanism for the physical side of things since you don't really regen mp that quickly without something external.