Why couldn't Dooku lead the attack on the Jedi temple?

So yes I get that Dooku doesn't have Anakins potential and Sidious never viewed him as a true apprentice, but why did Sidious have to wait for Anakin to fall to execute order 66? Why didn't he have Dooku lead the attack and then use that tragedy to feed Anakins negative feelings and bring him to the dark side. Since the Jedi are being hunted Padme would seem to be in even more danger. And Dooku is definitely strong enough to do it. I think this would have made Dooku a better villian and would have made for a better story.

Because in that case Anakin would be defending the temple, he'd go into the ZonRE and defeat Dooku. Order 66 would fail.

That would make even less sense. Palpatine made it seem to Anakin that the Jedi were in the wrong which is part of the reason why he was fine with betraying them. No way in hell would Anakin join Palpatine if he hadn't fallen prior to Palpatine executing Order 66.

If the Republic saw Dooku purging the Jedi it wouldn't matter what Sidious' sob story was, they'd burn him alive.

Because Sidious, as said already, already made it seemed justified to take over the Republic and enact exterminatus. He can't do those things by just randomly attacking the Jedi Temple. The army he needs still belongs to the Republic.