Is it possible to have order and peace and orderly
societies without hierarchical government
and political institutions?

Political institutions are the organisations in a
government that create, enforce and apply laws.
They often mediate conflict, make government policy
on the economy and social systems and otherwise
provide representation of the population.

Political instituions set the rules in which an
orderly society obeys and ultimately decides and
administers the laws for those that do not obey
thus hopefully preventing chaos and disorder.

Foxy
In answer to your first paragraph, yes; the answer is a benevolent dictatorship; however the drawback is that, usually as shewn by history, the next dictator is not benevolent.

Is Mise,

I don't believe in cults of personality, repression of
political opponents, suspension of elections and civil
liberties, and not obiding by the rule of law procedures.
American President Biden said it well when he summed
up the former president's actions:

"You can't love your country only when you win.
You can't obey the law only when it's convenient,
you can't be patriotic when you embrace and enable lies."

Foxy, you have exactly encapulated the life of Biden in his own words. His popularity stands at 34% now.

Josephus,

Actually as I told you on another discussion:

The national poll, conducted Jan 12-13 found that
45% of US adults approved of Biden's performance in
office, 50% disapproved and the rest were not sure.
Biden's approval numbers have hovered below 50% since
August.

At the same point in Donald Trump's presidency, about
30-39% of Americans approved of his performance in
office while over 50% disapproved.

Foxy
Biden is in the same boat as our republican politicians, a perjurer, they swear allegiance to the Queen and try to destroy the Monarchy in Australia, Biden swore to uphold the Constitution of the USA but is trying to subvert it.