Great post.
I think you're ignoring a pretty vital point here, which is that we usually played a midfield 2 during that time - in particular 2006-2008 - when all other big clubs played a midfield 3. Not even a hybrid of Beckenbauer-Maradona-Xavi-Gullit-Keane would be able to dominate a midfield 3 in a midfield 2. You say our play was mostly about our attacking players. Well, yeah, thats because we had one more of them on the pitch because we had one less midfielder. The midfield were tasked with providing the forwards with the ball, whilst mitigating the opposition's midfield dominance. Their role wasn't to dominate the midfield in those games. For it to be remotely workable against the best teams in the world it requires either two incredible CMs, or one solid CM (Carrick) and one superior being (Scholes). Put it this way, put any other top midfielder into that midfield two, and tell me they would dominate against the midfield 3s of the best teams in the world. He didn't have the same freedom or protection afforded to Pirlo, Xavi, Iniesta, Modric, Kroos, Gerrard, Lampard, Yaya, De Bruyne, Silva, Seedorf, Fabregas etc.
As for the two finals vs Barca, Scholes started neither as he was on the wane by then. Really his renaissance as a DLP was from 06-08 rather than 06-10. In 06-08 we won 3 back-to-back league titles and the Champions League. Scholes started the CL final, and scored the winner vs Barcelona in the home leg semi, and played the full 90 when we held the 2nd best team in the world at that time to a goalless draw on their own turf.
In answer to the OP, I think it's actually a shame that Scholes didn't get to play the majority of his career in a conventional midfield 3, as that would have got the absolute best out of him. He had all the skills required to dictate from deep, the skills to be impactful in the final third, whilst holding his own defensively. I can't think of any other midfielder who could do all of those things to the same level as Scholes. Xavi, Iniesta and Modric are amongst the best midfielders of all time but none had Scholes's finishing, anticipation in the box and long distance shooting. Gerrard and Lampard, the two other best English CMs, could not dictate the game from deep (ditto Jude). Etc.