Bringing along "X job" just for fun is what linkshells do. Pickup groups will never do that because there's this other guy that's on a better job and has better gear and he answered at the same time you did for the shout. Simple as that.
Even though I have 20 out of the 22 jobs capped, I only play three with any regularity. Two are used in different types of group content, and one is used almost entirely for solo.
No one expects you to have more than 2-3 jobs at max gear. There simply isn't enough room in our inventories for it.
I always suggest you level at least two jobs and gear them well: One job for yourself, and one job for everyone else. Use the job that everyone else wants to get gear for the job you really want to play. (And if that job is well geared and has a good reputation from lesser content, you'd be surprised at who lets you in. You ever see a PUP destroy things in NNI? You ever see a BLU tear some Delve mobs to pieces? I have. I also know those players have a COR and a WHM they used to gear those two jobs, and are willing to come on those jobs in big group content if required.)