It's not so much the continuity of the grand story arch, but the small details of the characters.
The best part of Avengers isn't that the story's led to the team-up, it was that the team up was of a bunch of characters you got to know beforehand.
Just wouldn't want someones first experience w/ the MCU to be to jump into Avengers, and then straight to AoU and then not see what made it all so special to begin with. It's the build up to the payoffs. The payoffs of course being the Avengers movies, and them most recently Civil War (which was Cap 3 and Avengers 2.5)
Even though Avengers and AoU are much better movies than what DCCU has produced so far, I wouldn't want anyone getting a BvS rushing to the promise lands vibe from it all.