Actually, the 2.0 Summoner quests are some of the few quests that explicitly require Main Story progress to continue. If you try to accept the Austerities of Wind quest before you've cleared Garuda (normal mode), the game will not let you. Same with Titan (and presumably Ifrit, even though that part of the story should be long done by the time you hit lv 30 SMN).

As for the Ultima Weapon thing, even though Ultima Weapon absorbed the power/aether of Garuda, Alphinaud explicitly states that the Weapon is a deterrent. There's nothing stopping the beastmen from summoning their primals again post-Ultima Weapon except fear that they'd just be eaten immediately. This actually proves that the exact same "quantum of aether" in the aetherstream is not summoned every single time a particular primal is summoned. However, it does not discount the possibility that all of "Garuda's aether" comes from a larger source in the stream and summoning her into the physical plane just draws a small quantity of it.