It wouldn't be right for Obi-Wan to kill Dooku, Anakin has to do it to prove himself to...himself. It's his personal vendetta against Dooku that allows him to win, via angry thoughts etc.
And I find the idea of Sidious watching, or just the Chancellor, Anakins trusted friend, watching as his apprentice (Dooku) and Anakin fight, very appealing. Anakin, like at the start of RotS is just expecting Sidious to encourage him, while Sidious is actually manipulating every event and has managed to find a replacement for Dooku.