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Had Yoda remained on Coruscant, Palpatine could not have pulled off his shenanigans, could he? There would have been no "B Team"; there would have been Yoda and Mace Windu showing up at his door. And this was a very narrow window of opportunity for Palpatine to pull off what he did, before the war ended and the Jedi went home.

What was Palpatine's original plan, given that literally the only reason why Yoda left at all was that somebody happened to bring it up as an afterthought in a Council meeting?

They could always blow up the Temple with a nuke.

^he needed the political will.

Does nobody consider that Sidious waited until Yoda was off of Coruscant to tell Anakin?

Apparently, the RotS novel elaborates on this; the Jedi purposely sent agora away to try to bait Sidious out of hiding. Which does not explain why they did not have any sort of apparatus in place to actually follow through and quickly alert the Order of Sidious's presence. Windu should have immediately made the connection that if Dooku is serving Sidious, the war and the clone army are scams, and that the latter is so obviously dangerous to the Jedi. Yet, Windu only warns Yoda, not the other Jedi so faithfully fighting alongside Palpatine's army.