Basically, half the citizens of Zanarkand were walking along one day and all of a sudden, they fell in a plot hole and became able to summon.

It's likely that summons never needed Fayth in the first place, but in revenge for the war, Yu-Yevon makes it the case because he wants to send Spira into that Spiral of Death that forces two people to completely give themselves up to defeat Sin (a Fayth is nominated and the Summoner dies). After the Final Aeon is created, it seems the Fayth becomes Sin until the next Final Aeon; if Yuna had defeated Sin by "conventional" means, the next one to complete the pilgrimage could have found Jecht as an Aeon if they'd looked in the right place, but it was never to be.

This also means that Valefor, Bahamut and definitely Anima, along with all the others have been Sin in the past. How the Magus Sisters came to be is questionable, but hey, Yunalesca never said how many people had to give themselves up to form an Aeon.