I'm gonna call bullshit on this one. Simply because, just imagine what would've happened if Anakin didn't stop Windu.
Imagine if you will, a scenario where Anakin just bugged out after Mace told him to wait in the Jedi Council Chamber. He goes off, takes Padme and the droids, and he fucks off to Naboo or something, leaving the whole war and the Jedi Order behind to raise his kids. Windu goes over to Sidious with his strike team, Sidious puts up a good fight and kills the team, but Windu with his Vapaad mastery wins the day and Sidious dies. What happens after that?
The movie has established that the Senate LOVES Palpatine. So much so that they kept voting him in, FDR-style, despite the fact that his term limits are up. What exactly do you think will happen to the Jedi Order once the Senate hears that a Jedi High Councilor just killed their beloved Chancellor? They'll go nuts. Not only will they not believe the Jedi when the Jedi accuse Palpatine of being a Sith, they will issue Order 66 themselves, seeing Windu's assassination of Palpatine as a naked grab for power. And the clones, being the obedient little children that they are, (they're literally 10-year-olds in the bodies of adults) will wipe out the Jedi Order.
Windu and the other Jedi on Coruscant will get overwhelmed and slaughtered by the 501st and the Coruscant Guard, the former of whom were already planning to wipe out the Jedi, the latter were zealously loyal to Palpatine. You'll still get the same Order 66 montage of the Jedi getting wiped out from across the galaxy, and whatever few survivors are forced into hiding. Sure, Obi-Wan and Yoda can stage a counterattack to Coruscant, but what will they be going after? The Senate? What, will they hold whoever gets elected to replace Palpatine hostage and have them rescind Order 66? That would just add more fuel to the fire and prove to the Senate that the Jedi were trying to take over illegally. That will just fuel the people's hatred for the Jedi and make them hate the Jedi even more.
The only difference is that, with Palpatine dead and Anakin gone, no one is there to assassinate the Separatist leaders. They're still on Mustafar, awaiting orders. And when they realize Sidious is gone, they'll just do whatever they can to keep their power, but with the Republic being more focused on hunting the Jedi, the Seps will have some breathing room, especially with their quintillions of droids still active. But here's the kicker: the Seps HATE THE JEDI. For years, they've seen the Jedi as the toadies of the Coruscant elite. So there's no way the Jedi remnants can hide out with them, especially with the likes of Gunray and the other Jedi-hating Sep leaders still being alive.
At most, some of them might allow some Jedi to defect to the Separatists, IF they promise to be good little toadies and serve their needs; I can see someone like Wat Tambor allowing a few Jedi to seek refuge in Techno Union territory so long as they bend the knee and serve, but most Separatist citizens hated the Jedi even before the Clone Wars, so most of them won't accept Jedi refugees, and will more than likely shoot them on sight.
And the third and most worrying thing of all is that the Republic might die. Without Palpatine to hold them back, the Seps will just vote to keep the war going, and eventually, Kamino won't be able to keep up producing clones for the Senate whereas the droid foundries within Sep space can and will keep farting out droids. Which eventually will lead to the Republic slowly collapsing and falling to the Sep leaders. Get ready for a galaxy controlled by corporate kleptocrats who will rape and pillage worlds for resources and slaves. Basically the Empire, but imagine them having even more endless amounts of soldiers thanks to their droid armies. So basically, the Rebellion would be even more fucked because they're not dealing with a human army that gets tired or has people defect from it, but rather, they're dealing with an endless tide of droids that don't get tired, don't need a break, and will keep coming until the enemy is dead.
Either that, or the Separatists might reach a compromise with the Republic, but both sides will still be corrupt; you'll have Palpatine's supporters on the Republic side, and the corrupt corporate leaders on the Separatist side. Imagine them forming a new state together; neither side will be favorable to the Jedi or to people who don't want a strong, overbearing government. Tarkin and his mates will crush any dissent within Republic space, while the Trade Federation and other corporate bodies will ensure that any dissent in Confederate space gets squashed. Which means that again, any future rebel movement will be even more fucked than they would be under Palpatine.
Really, galactic liberty died when Mace Windu made that ill-fated assassination attempt. The right move would have been to investigate Anakin's claims so that you'd get proof, or at the very least, leak it to the Senate. Palpatine's top man, the Hero with No Fear, accuses him of being the Sith Lord who's been playing both sides against each other? That would destroy Palpatine's political capital, especially given how it's Anakin making the accusation; everyone knows that the two of them are close friends and Anakin is a strong supporter of the Chancellor. So it's damn near impossible to dismiss that charge as baloney.
Leaking Anakin's accusation to the Senate will cause chaos and sow distrust among Palpatine's loyal senators, and it will give Bail Organa, the Delegation of 2000, and other senators who have their doubts about the Chancellor some much-needed ammo. Padme would obviously back up her husband's claims, knowing him to be an honest man, and that would be another sore spot; Padme is Palpatine's former master when she was Queen of Naboo and he was just one of her advisors.
Eventually, the Senate will move to strip Palpatine of his powers and detain him so they can investigate the matter. If Palpatine tries to use the clone army against the Senate, that would also end badly, since as Bail Organa said in EPIII, too many systems are too well-armed, and the clones themselves are already getting stretched thin fighting the CIS. Once the Senate finds enough evidence (Labyrinth of Evil shows that it's possible to figure out the truth about Palpatine with some detailed investigations) they'll issue Order 65, and have the Chancellor executed. And sure, Palpatine might be able to put up a decent fight, but I'm sure a turbolaser blast from a Venator can atomize him and end the threat.
Mace Windu is more disciplined and wiser than Anakin, able to use the Dark Side without falling to it. But at the end of the day, he shared more than a few negative traits with Anakin, that being his hot-headed eagerness to end the threat, without looking at the consequences. At the end of the day, Mace Windu is just as much a loose canon as Anakin Skywalker is, and his actions, along with Anakin's, doomed the Republic and the Jedi Order.
