If you want entitlement to a court on the legality of content before getting cutoff from service, negotiate a contract that specifies that you can carry any legal content, and the other party must assume content is legal absent a determination by a court to the contrary.
OTOH, that’s not part of anyone’s boilerplate, and adds a lot of potential cost, so expect to pay an extremely hefty premium to get a business to agree to those terms.
Which is what provides checks and balances, AWS says "You violated our ToS, we're cutting you off", "Parler sues and says 'No we didn't and here's why'".
If Parler wins and can prove that they were unfairly targeted, then they can sue Amazon for damages. Which is what keeps Amazon from unfairly applying its ToS. And if they can demonstrate irreparable harm, then they can get an injunction forcing AWS to restore their services immediately rather than waiting for the court case to be decided.
But I think the best they could do is present monetary damages, which the court could decide AWS is able to pay.
https://www.cnn.com/2021/01/11/tech/parler-amazon-lawsuit/in...
In fact this new form of justice is so efficient we can even shut down a company before the court proceedings have even started. By we I mean our corporate overlords, but they wouldn’t ever turn on us.
This isn't a new form of justice, this is how the civil legal system works.
Did Parler promote illegal content? Again, Amazon is NOT a Court.