Initially I held the same view that Steamboat Ricky just posted. That whoever won the match would then be considered the top guy in the company, their belt made to look stronger and the loser have their belt appear somewhat of a level between the US and Intercontinental Championship belts and the winning title.
However, to be honest with you, I believe that even with Smackdown's victory in the Bragging Rights match (not necessarily how they've won) that the RAW brand is promoted in such a way as it is the WWE's "flagship" show and that the WWE Championship is already ahead of the World Heavyweight Championship as a natural consequence of that.
I do agree that the WWE doesn't consider the ECW championship anywhere close to the level of either of those two belts. Sometimes, I doubt whether it even has as much validity as the Intercontinental and United States championship belts. The perfect example to this, and it may only have been a storyline but it really cheapened the belt to me, was during the Hardy Vs Hardy feud last year.
If you recall, entering the feud Matt had just come off a very successful reign as the ECW champion where he was supposed to have elevated the title. I thought he did a pretty good job of that. However, his reasoning behind attacking Jeff when Jeff became the champion was that he was jealous that Jeff had won the big one and he hadn't really accomplished jack. That's how it came off to me. His very recent (before that) reign was brushed aside and never mentioned. To me it cheapened his reign and the ECW belt in the process because they made it insignificant for the purpose of the feud.
In so far as a champion of champions match was held, I agree that it would be the perfect main event for the Bragging Rights pay-per-view. If the WWE is ending the ECW brand then it would still work as a RAW Vs Smackdown match. If booked correctly it wouldn't separate the two brands further than they already are but would enhance the champion.
If I were to book it, I would either make it a massive headline show that would get major buy rates (say HBK/HHH/Cena Vs Undertaker) or I would have a young champion be put over (Cena/HBK/HHH losing to John Morrison (Smackdown); or Kofi Kingston going over Chris Jericho (RAW). I would do the latter one because it would really work hand in hand with the youngster winning the championship for the first (or second, etc.) time in their young career against an icon.
There would be no need to eliminate the RAW Vs Smackdown team match. I would also include a US Vs IC champion vs champion match and a Diva Vs Womens champion vs champion match.
The four major matches on the card would feature heavily championships and the Bragging Rights cup. It would be the pay-per-view where you would get all of the major names of each show facing each other, which was the intention to begin with.
Great thread.