Green Goblin is a very important figure in Spider-Man's mythology. I see Webb being very faithful to the characters and their story arcs. I have doubts he won't use the Goblin in later films.
However, if he doesn;t, it won't be the end of the days for me. I will have nothing against that as long as I'm satisfied by the way the story is told. After all, it's always same story told differently.
Then again, Webb several times confirms the significance of Oscorp to Peter and even connected his paresnts' past with the company. He also included Van Atter, even though I don't see him turning into Proto-Goblin. There is no guarantee of that, but there good signs it will happen.
I have a good feeling Green Goblin will be in this trilogy, but what actually matters is how he will be handled this time. I would really love to have Ultimate Osborn merged with the 616 Goblin.
I also wonder why Webb linked Peter's parents with Oscorp. And here is what I think:
By connecting them with Oscorp, Webb also creates close relation to Osborn. Thus, we have Parkers connected with Osborns. If so, won't Webb go with the Ultimate route, but in a different way and turn Brocks from comics into Osborns in films. Not characters, but the connection between them. If Osborns appear in the next film (which is very likely to happen), then they'll surely become a part of Peter's life. What's interesting is that they can already be a part of his parents' lives, leading to Peter having a much more complicated conflict with Osborns. From one point he has Harry as his first friend, from another he has Norman, who wa sinvolved in the detah of his parents, even if indirectly. This puts much more stress on the way Peter will try to handle the relationships with both.
So, I can see Webb choosing to have the Goblin's serum as a cure to something that was being developed by Parkers and Osborns (and maybe even Connors, consequently). Osborn, as a businessman, decided to get rid of the couple of scientists who asked for too much and claimed the ownership of the serum. Now, Osborn is trying to finish it on his own, even if unsuccessfully. Because of his mistakes, the cure becomes the serum he takes, leading to his transformation into the Goblin. Meanwhile, Peter and Harry, initially not really getting along so well, grow to become close friends. Osborn, having learnt about that, tries to use Harry to get to Peter, the son of the people who actually created the cure.
This pretty much well combines both 616 and the Ultimate, as well as draws a line between Parkers and Osborns.
But this is just my speculation and it may have flaws, especially in the implementation of it.