Rydia was Summoner that could use Black Magic and some White Magic but she never specialized in affliction magic.
Affliction magic? ...Do you mean Black Magic, which Bio always fell into? And are you already forgetting Physick and Resurrection, which are healing magic, which kinda falls in the White Magic camp? Are you complaining that Summoners have all the tricks of the trade?
Looking at the source material of the Summoner is race of people born with the power of Summoning that has Black Mage or White Mage as a secondary job.
Only two games featured Summoners as a race...try again. Secondly, Summoners of 14 have offensive and supportive abilities. Your reference to "source material" never seems to include the current game, which is the point. Final Fantasy games have no continuity in lore. Dagger and Eiko were Summoner/White Mages, so Summoners should be Conjurers in this game. See, I can do it too.
Not true all classes/jobs used past Final Fantasy titles as their source material for lore the only exception is the Summoner in Final Fantasy XIV. Dagger and Eiko's primary job was a white mage while their secondary job was a Summoner but when the Summoner is the primary job then the Black Mage is the secondary job.
Rydia only used two spells from the Summoner we have right now which are poison and bio which correspond to bio and bio II that's it from the affliction mage the rest of her skills are mainly Black Mage abilities with a few cure and resurrection spells from the White Mage
Square Enix should give the Summoner the ability to absorb the Egi and summon the Primalsc with a reasonable cost.
So you're basically saying, Poison and Bio should go to Black Mage and Summoner should only have summons. Thus Summoner should have no attacks only summons, that come in do one big attack and go away until you can get mana back. Then you can just use Mage's Ballad for all your MP back and do it again. Sounds like you'd make a great FFXI dev.