A mission-by-mission tutorial also robs those STFs of a bit of their wonder and mystery for new players (I can remember when I was new to STFs and piecing together what triggered what when and why, and having great fun trying to puzzle it over), so there's that trade-off, too.
Just my two cents.
I was thinking making it more bare bones. Like for Infected Space, the tutorial would be a transformer with a pair of gens and a sphere guarding it, and that's it. The player would be walked through the process (kill sphere, kill gen, nanite probe spawns, kill spawn, etc) and be taught rough terminology (what the 10% rule is perhaps) rather than a full scale version of the mission. Play it off as things Omega Force has seen while fighting the Borg, without it being EXACTLY the same. That way when they get into an STF, the player will see a transformer with a guardian and go "oh, I remember that" and act accordingly.