But it was the only method they had. As I said above, no legal method would have worked. The Jedi had only circumstantial evidence connecting Palpatine to Sidious and his "confession" to Anakin (in which he didn't actually confess to anything specifically) would never hold up in court or the Senate. Bringing legal measures against Palpatine would fail, as he had too much control over the legal institutions and could quash the Jedi and their Senatorial allies with his increasing political powers. He could even fabricate some excuse to blame the Jedi for the Clone Wars and initiate Order 66 at any time. By the midpoint of Episode III, the Jedi existed at Palpatine's whim and he awaited only an opportunity to turn Anakin to destroy them.Ghost Rider wrote: Given there were still people who opposed Palpatine...going the extra legal route was the dumbest thing to do since, he could literally insure that people will follow his side. Hell, it gave him fuel to tell people one of the organizations they trusted, tried to kill their beloved chancellor.
That is why he won, they played into his hands, and they did so like dumb sheep. They were some arrogant that it took them years to even acknowledge the Sith lord problem and by then they had not clue one what the fuck he was doing and opted for the only method they thought they had.
On the other hand, if the Jedi went to Palpatine's office and assassinated him, they win. Game over. Sure, the aftermath would have been messy, but dealing with the fallout from a dead Palpatine would have been infinitely better than dealing with a live Darth Sidious who commands the entire galaxy and an army of clones loyal to his every word.
The only thing wrong with Mace Windu's plan to kill Palpatine was that he failed to kill Palpatine.