That image is so weird. VII didn't have any summoners, just summons. I guess in theory you could make your own summoner if you want, but it wouldn't be very efficient, high cost, very squish.
VIII, why is Phoenix displayed? It was one of very few things you couldn't directly summon. And also, still no summoners this game.
Summoners in IX were just White Mages with summons.
Why is X-2 Yuna next to Anima? They couldn't even get the games right on that one. And again, summoner just tacked onto white mage (although in a much more expanded role I guess).
XII had a good set of summons, too, but still no summoner. Plus I don't know of anyone that ever consistently used/relied on them in that game.

Summoner has always struck me as a role with a very loose definition. And most often that depends greatly on the story of the game. I don't really mind it as is, but sure, there's plenty of other designs they could've used. Maybe it would've been cool to use "summons" as a stance. Ifrit-stance, Titan-stance, etc. Skills adjusting accordingly. Idk. But, this is what we got. Probably they didn't want the class to seem totally useless if the pets die, so probably better to not make the class completely reliant on them.