My first time in the Strike in the PC Beta, I was matched in right at the end. While I've played it before, I can only imagine how disheartening that would be to a player who is playing it for the first time. They're missing so much. Edit: To be clear, I mean just the first time. So, having some kind of permission in place so that players only can be matched in progress after finishing the Strike for their first time.
While I do agree with your idea? Setting up a permanent lobby for a single usage, from a programming perspective, is a complicated task in and of itself. The entire reason you limit so many matchmaking "option setting" variables is because many of those have the potential to crash connections. This is going to be a long and complicated explanation, but what I would specifically recommend for a full game is exactly what Destiny already does: Minimal join in progress potential for the strike itself from the manager. Accessing the playlist is built in with JIP. That and new players would ideally react like most would: You are at the end of the strike, but you are not new to the world and it's mechanics. It's a mid level event after all, there is no strike you do before the first couple of missions. So? You're not finishing a short strike... your reinforcing a team of guardians who need assistance or could use additional damage potential.