I think this has been suggested in other ideas people have shared here over the years, but by showing Dooku in TPM you could also play around with the implication that he is the “master” Mace and Yoda speculate about. It would be interesting if Sidious=Palpatine could be more of a twist, where we actually never see Sidious until Palpatine reveals himself to Anakin.

A Pro would be that Anakin could blame Dooku for indirectly causing Qui-Gon’s death if he thought Dooku was the master of his killer. And, the prequels could play out in an interesting way if “Who is the Sith Lord” was more of a mystery.

On the other hand, you would have to cut a not-insignificant amount of runtime to cut all of Sidious’ scenes. He has quite a few with Nute Gunray in TPM, but only one in AOTC (but his one scene is important because it reveals Dooku’s Sith name, which helps add clarity to the cloning mystery) and one in ROTS with Grievous.