You're missing the point, though. Yes, AC wasn't necessary, but neither was The Hobbit. In fact, Tolkien only wrote the LOTR trilogy at the request of the fans that loved the Hobbit. How it was handled is a different matter. Whether fans liked the outcome or not, they are the ones who asked for the Compilation. Square most likely never intended making the Compilation, I agree with you there, but that doesn't mean tha they don't work well.

As much as you'd like to believe that an extensive overview of Vincent's past is scattered in FFVII I can assure you that it is not. I haven't gone so far as to write down every bit of dialogue. But I've played through that game at least 10 times and I've done every side quest you could ever dream of. There's Vincent's flashback, and then there's a little bit more when you take Vincent to Lucrecia's Cave for the first and second times (considering the second time is when you are on the Third Disc).

There is nothing wrong with a sequel as long as it can agree with the original, which the new ones pretty much do. In Advent Children, everything is consistent with the game. Tainted Lifestream exists because Jenova's cells have seeped into the Lifestream and caused it to be tainted. This is also what causes Geostigma. Break that word down and you get "mark of the earth" which makes sense. Lifestream is from the earth, but the tainted Lifestream causes this sickness (characterized by a stigma on the skin) in all who carry it. Why? Because they are carrying Jenova's cells and very few people can accept them. In fact, only those who have first been exposed to Mako can accept Jenova's cells. This is perfectly consistent with the original game.

See how the new idea of tainted Lifestream was caused by the events of the game? And then you layer on the true story of Cloud releasing his guilt, with a pinch of side plot, that being the Shinentai of Sephiroth, and viola. You get AC.

With DoC, they took the basics of what we knew about Vincent's past already (i.e. Turk, Lucrecia, Hojo, Jenova Project, guilt) and they embellished on them. That doesn't make it inconsistent with the game, it just gives us more detail than the game did. That's all. The addition to Vincent's past is entirely consistent with the original game. Whether it was intended or not is not the point. You are claiming that you are angry with the inconsistencies and the plot holes, so I'm showing you why the Compilation is neither.

Now, about the Stagnant Lifestream, I cannot say. DoC didn't give us many clues about it's origin, use, or how it is controlled. It obviously has something to do with Vincent, considering that Lucrecia was studying it as part of her research on her thesis on Chaos, which she later applied to Vincent. We also know that Nero has some control over it. How or why we do not yet know. How the Stagnant Lifestream applies to and effects Vincent is not yet known. Perhaps it is just a mystery where we must suspend our disbelief, or perhaps it will be explained later on, but just because it didn't exist in the original game, doesn't mean that it's inconsisten with it. There's a difference.