I pretty much sure that if you have a summons you can summon it whether someone else in party has it or not. Remember you will have to be summoner and go on quest to fight and win that particular summons. And from what I hear you will have to be level 60 to beat the strong summons like Ramuh, IFRIT to obtain.
So not everyone will be a summoner. Plus groups will not except too many of the same class. So most often than not you will see not that many summoners in same party. But will have a mixed of all classes to have balance party.
A powerful party will have almost every class in group. You will have variety.
Summoner class has been made to work for online play just like every other job. You won't be seeing tons of summons all over the place. They will be work just to obtain, many won't want to work that hard to get them. I may have to change my mind to another advance job myself. Because I want to be summoner but it seems alot of work.