Unfortunately, since FFX it indeed has been a pet class - having said that, pre FFX summoning was little more than a flashier magic spell with a nice graphic/animation. That style of spell worked well for the older games which had strict turn-based combat, but in more modern action orientated titles, that seems decidedly old-fashioned, especially as battle is usually far more feverish than it once was, thus summons remaining on the battlefield.
And the kicker is the player would never be able to call forth 'beings of immense power' as you termed them, as how the game's lore has been written, just does not allow that. Primals require enormous amounts of aether to summon normally, and require multiple summoners summoning at once - the actual player SMN Job is simply a short-cut that is summoning a slither of a Primal's essence that assumes a rough imitation of the Primal.
DRG isn't getting a wyvern in XIV - again the game's lore wouldn't allow that even if it was considered. And RNG is traditionally just a glorified ARC with extra sniping abilities. I don't know where you got the idea they're a pet Job.
Although it's obvious the player will be getting more summons in the future, it's firstly dependent on SMN's abilities altering those of it's base class (ACN) - apparently this is half the reason why Ramuh and Leviathan aren't being given 'egi' forms for SMN yet - because Jobs only have five Job abilities, and ACN only has two for summoning, with the third given by SMN, they would have to spend a lot of time altering and re-balancing SMN's ability structure in order to accommodate extra egis. So it's more likely you won't see extra summons til at least when the level cap is raised (sometime next year I imagine).
The SMN's Primal-egis already do this with the level 50 SMN Job ability 'Enkindle' - makes the egi use their parent Primal's 'signature' spell/move. And because that ability can only be used occasionally it keeps the spells balanced. This is what you're not understanding - single player FF titles are different from an MMO in that the developers can get away with having incredibly powerful spells and abilities, but in an MMO, classes and Jobs have to be properly balanced so as not to break the game by giving one Job or spell more potency over an other, an important part of ARR's whole design.
That's just not possible I'm afraid, given a Job uses it's base class's weapon, and due to the Armoury System used in XIV, each class is identified with only one weapon type - SMN's weapon type is grimoire. Wooden staves are the weapon type for CNJ/WHM and metal rods are THM/BLM I'm sorry to say. It's a restrictive system to be sure, but that's ARR's Legacy which players actually voted to keep - one of the first things Yoshi-P asked the Community when he took over as Producer and Director was did players want the Armoury System scrapped in favour of a FFIII/V/XI/Tactics style Job system, or to keep the Armoury System with it's classes identified by a weapon type and just add Jobs as an extension of that. Players voted for the later. So yeah, that's democracy for you.