Job Framework: Beastmaster

[Seraphor]

That makes no more sense than to say that Summoners could never have been a real job because they have to acquire summons...

There's a lot more to it than that.
For starters:
They can barely work out how to make SMN's pets work, they're not likely to want to open up that can of worms AGAIN with another job. SMN's pets have now lost HP and hit potential.
They've limited SMN to just three Egi's, because balancing multiple sub-jobs in this game isn't possible. So unless BST only has one or two pets....
They've already suggested Beast Tamer and Puppetmaster as potential limited jobs.

Plus 'summons' have been acquired in a number of ways throughout the series. BST, like BLU is iconic for taming it's own pets.