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.
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I joined in at Phogoth my first time playing Destiny and started yelling "HOLY SHIT LOOK AT THIS -blam!-ER" it was a good experience, 10/10 didn't mind going through the boring midparts.