@GlobalHumanism
The beliefs of the Kharijites, while attractive on some level, would in practice lead to chaos.
1) They believe that the act of sinning constitutes unbelief, and therefore a person who sins is outside Islam.
2) If the leader sinned, it was the duty of Muslims to oppose and depose him.
Problem is, who decides what is and isn't a sin? Virtually any disagreement over any matter can be inflated to a matter of life and death, with people not merely being wrong but being apostates. It's great that they would oppose tyrannical leaders, but by the same logic they might just as easily oppose a wise and reasonable leader. What if the leader takes a decision they didn't like, or disagrees with them over some point of theology? It's a recipe for absolute chaos. Any lunatic could potentially claim the leader is an unbeliever and start an insurrection.
While the belief that Islam is defined by actions is attractive (and theologically correct), again it is open to abuse because who decides what is Islamic? Once again, we end up with absolute chaos, because people will be declaring each other unbelievers whether Shia, Sunni, Wahhabi, Salafi, Sufi, Ibadi, or whatever else. This takfiri extremism of the Kharijites is dangerous.
On balance ironically perhaps Islam is best served by Secularism as at least that guarantees everyone equal rights before the law. Matters of religion are personal; and when it comes to actions of a leader, regular Islam already makes it clear that one must struggle against oppression. But randomly declaring takfir on anyone who disagrees with you is not the right way to go.