I think it was wise to have the big appearance by the entire original team saved until the end. It's similar to Star Trek: The Next Generation : they had the McCoy cameo in the first episode, then it wasn't until Season 5 or so that Spock and Scotty popped up, and they didn't even deal with Kirk until the first STTNG movie, after the show was over.
The origin story had Egon, Janine, and Slimer in it to “ease” the new characters into the story. Those three certainly made plenty of appearances over the course of the series, but they weren't the focus and shouldn't have been: the show was called Extreme Ghostbusters not The Real Ghostbusters Phase 2.
It wasn't until the new characters were well established, familiar enough to make the meeting really meaningful, that it was time to bring back Ray, Venkman, and Winston, and see what happened.
Like a lot of people, I have to assume that if EGB had gone onto a second season, the other three original Ghostbusters probably would have popped up once in a while now that they were part of the scenario. But of course, since the show didn't go on, that wasn't given the chance to happen.