I haven't seen amazon claim that Parler broke the law. They have a TOS policy that forbids the hosting of illegal content.
> Has it been proven in court?
If a AWS customer is hosting child porn, does AWS take it down as soon as they're aware of the content, or do they wait for a court ruling?
> Or did a private company decide that on their own? Why should they have that power?
It's not power. You have a responsibility to exercise your judgement, and avoid participating in criminal acts. If you knowingly participate and profit until there's a trial in court, then you're an accessory. Section 230 has some exemptions -- you aren't protected if you maintain illegal content.
What happened on 1/6 was an armed crowd breached the capitol building. A plain reading indicates that this is an act of war, and AWS has enough legal problems without opening themselves to charges of aiding an enemy of the state in an act of treason.
This isn't "power" it's a matter of legal responsibility.