As I said, they just needed to trust the wisdom of the Jedi :D.
And in general, look at how Palpatine treated his former apprentice:
He told Anakin to simply kill him, and Anakin obeyed like a puppet.
And regarding Tatooine, I disagree with you, because the Council refused to train him as a Jedi, not to take him from Tatooine.
Dooku was initially planned as a pawn, and as soon as it became possible to replace him for his own benefit, Palpatine did so... The Separatist army was commanded by Grievous, who obeyed Palpatine unconditionally, and Dooku was discarded to increase the influence of the Dark Side on Anakin... A normal person would not have killed Dooku... and in comparison to the situations between the defeated Dooku and the defeated Palpatine, Dooku looked completely incapable of anything...