Yeah, what about them, once you collect them which is optional you can just replay the levels to get high scores, aside from the first 3 missions which have the flashbacks, but even those have combat. The traversal stuff is like :30 seconds between pure combat encounters.
Secret rooms are for fun, onc eyou do challenge you don't really replay them, not any different than they were before.
Cutscenes aren't an issue, it takes two seconds to skip, and yes its fine to have little story parts and still be an arcade like experience. Not sure where that requirement comes from.
And lastly the Trade Mission, its short and sweet, and the reason its separate is because if you put it with anotehr mission then it would become tedious to do this intro every time you replayed that mission. The funny thing is the next mission is the longest mission in the game and its about 20-22 minutes on DMD for most players, so actually DmC balances out the Trade by having the next mission be twice as long.
The bosses on missions by themselves are amazing as well, because its fun to just replay them and style on them as you'd like. Hell, I'm super happy Metal Gear Rising realized that was a good idea, because the PC version I'm getting next week has an option to replay boss battles.