Basially the title.
Reintroducing a strike a great for the game. Making it a part of your seasonal story works fine as well.
But for -blam!-'s sake don't make people join into the middle of it after much of the strike and its associated story elements have passed. That is absolutely terrible for story progression and spoilers.
Forcing people into a matchmade piece of content for story progression is questionable to begin with, but losing a good chunk of the story because you joined in the middle of the strike? That's just terrible.
If you must put matchmaking into your story missions then disable join-in-progress, at least for people's first time through the story content.
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Yes solo or fireteam only (private) option would be fun and amazing.