All that matters is that Dooku was once a Jedi and a student of Yoda's but now he's not, end of story; anything more would be superfluous and only serve to slow the pacing of the movie down with useless information.
Like that scene where Palpatine talks about Darth Plagueis, a character who we never see or meet? They could have just gone with the trailer exchange and say the dark side of the force saves lives. Why talk about Darth Plagueis at all if the whole point is that the dark side will save Padme? Do we ever hear about Darth Plagueis again in the movies, or any other information that would make that conversation relevant? No. For arguing that Yoda is a side character and not the story teller, Palpatine sure does a lot of story telling for a side character himself. Only the difference here is that talking about Dooku is more relevant to Anakin's story since Dooku was a very promising Jedi who betrayed the order and went down his own dark path. Since everyone believed that the Sith were gone and it would be impossible for them to return, Dooku becoming a Sith should have been seen as a wake up call to everyone that any Jedi can become tempted, even the ones who hold so much promise. But instead of delving into any important details like that, we instead spend time talking about a character who isn't even in the movies and was actually replaced with a freaking half alien half robot contraption who's more useless than the ice cream guy in ESB.
And don't discount the Jedi order either because it plays an important part in how it shapes our main character known as Anakin. The movies spend a lot of time telling us what the Jedi can and cannot do, and it's the least good sounding thing in the whole series. You're not supposed to love someone, you're not supposed to feel attached to anything or anyone and you're not supposed to worry about the well being of others. You have visions that someone might die? Let them die. Death is a natural part of life, so why worry? Be happy that they had a chance to die and become one with the force. Let go of everything you fear to lose. Because if you start to worry even for a second, you'll become the single most worst thing in the whole galaxy. As Yoda says even in ESB,
Yoda: Once you start down the dark path, forever will it dominate your destiny.
That's what the Jedi teaches Anakin and that is what Yoda and Obi-Wan preach. The Jedi order is a freaking Dogma. They see their way as though it was the absolute truth and there are no other alternatives and no compromises. And this is the order that we're all too happy to see coming back?