Mace and Palpatine:
The Jedi had a made a choice about how to handle the Sith in Episode I, they were going to continue their long war against them and take them out whenever they appeared. What is not being said here is that Palpatine was the democratically elected leader of the Republic, a government the Jedi had sworn to protect and its laws they were upholding. So to go so outside that law, to take justice into your own hands is vigilantism and against the law, and in a sense is as much of a threat as the Separatists. The Separatists were an external threat but Mace was laying precedent for an internal one.
So, if Palpatine had been killed by the Jedi, who is to say that the next time the Jedi encounter a leader they disagree with that they murder them? Would Mace and the other Jedi stand trial for murdering Palpatine? Who holds them accountable? Is everyone just supposed to take Mace’s word for it?
This is no longer canon but at one time it was: Jedi coup from Wookieepedia (Natasi Daala entry): Shortly afterward, the Jedi Council now under the leadership of acting Grand Master Saba Sebatyne, formulated a plan to launch a coup against Daala. The Council put their plan into action at the same time as Senator Treen and her allies launched their bid to remove the Chief of State.
The idea that Mace had to act ‘immediately’ makes little sense, outside of it’s a two-hour movie and they have to push the plot along. We know there was a contingent of Senators that were pushing Palpatine to finish the war and to let go of emergency powers. Why didn’t Mace talk to any of them? If anything, with General Grievous dead, it weakened Palpatine's rationale to continue the war and possibly could've made the similarly duped Separatists leaders open to negotiating a peace deal. Why not allow the democratic process to work? If one says that process is broken, corrupt, and stronger measures are needed, well, isn’t Dooku making a similar kind of argument? The system was likely imperfect but that was the system in place, the system the Jedi up to that point had allowed to fester or limp along. And it was the system the Jedi were leading millions to their deaths in defending.
Mace played right into Palpatine’s hands and his rash actions gave credence to Palpatine’s claim that the Jedi were trying to take over because they had just tried to assassinate him. Palpatine manipulated the entire Jedi Order for the most part.
Jedi younglings:
So what kind of mutual agreement do you think the Jedi could come up with that would be satisfactory to you if it was your children? This is something that Lucas glossed over, but the potential was there to explore this further. We saw what Anakin being taken from his mother-by his choice (but this is like a little kid who is making that decision and a desperate mother who wants a better life for him no matter what), did to him, how it set in motion his dark path. And even the Jedi said he was too old to be trained. In essence, he had too many memories of his past, of his mother, so that the Jedi wouldn’t be all that he ever knew or could relate too. Now when I think of that, that’s similar to the First Order’s Stormtroopers. Albeit, they are likely much more callous in gaining recruits, but they are taking children very young and training them in their ways regardless.
Jedi and Politics:
The Jedi voiced disdain for politics did not stop them from playing politics at times. Nor did it stop them from defending the Republic some might have criticized. I’m skeptical that Lucas intended for the Jedi to be more involved with politics. I could see him feeling the Jedi needed to be more in tune with life itself, not so rigid with their rules and regulations, and to allow more humanity, to learn how to balance attachments and their desire to serve the Force and the galaxy. But perhaps there is also a criticism of the Republic’s representatives and citizens who mostly allowed Palpatine to manipulate them all into tyranny.
Palpatine’s megalomania:
I take this from Wookieepedia’s non-canon section on Palpatine:
His acts as a loving politician and later a helpless victim served only to bolster his true persona, that of Sidious. The Dark Lord was a highly manipulative, Machiavellian, exploitative and seductive megalomaniac, easily bending others to his will in his quest for Sith supremacy and ultimate power.[15][165] A narcissist, Sidious identified his own essence with the very blackness of space,[178] even going so far as to declare himself the ultimate personification of the dark side.[165] Sidious also displayed traits of psychopathy, including extreme sadism and cruelty, taking considerable pleasure in the suffering and deaths of others.
This passage is how Lumiya viewed him:
Though she was once fiercely loyal to Emperor Palpatine and Darth Vader, Lumiya developed a strong sense of disdain for Palpatine and viewed Vader with pity. Regarding Palpatine, she informed her future apprentice, Jacen Solo, that Palpatine/Darth Sidious was "a psychopath consumed with power," and that Vader had been "a sad man....whose one anchor to the world of the living was, yes, a galaxy-conquering madman."
Those are not in the canon sections, but at least in the past, someone was describing Palpatine as a megalomaniac.