@raphjd
I don't think you got any of your analysis right there, though the news report that the suit was being dropped is interesting and I thank you for sharing it.
Still... funny thing - Facebook does not use AWS for any of its own hosting (although some 3rd party FB apps certainly do).... Not only does FB have its own datacenters, it even builds its own servers (after all, it is a major contributor to the Open Compute Project). Then there's the fact that they moved all of Instagram's storage OFF of AWS when they purchased the company...
Twitter, on the other hand, has moved virtually all of its infrastructure to AWS. (Just to complete that part of my answer). So, my above statement that you got everything wrong is now, demonstrably flawed....
ALSO: It may shock you to learn that AWS is NOT the only cloud platform provider! When they de-platformed Parler, there were dozens of other platforms to which they could have moved: Microsoft's Azure, Google Cloud, IBM Cloud, and Oracle Cloud to name the BIGGEST.... then there are dozens of 2nd-tier cloud providers (my personal favorite is LiNode.com - they host all of my own servers!)
I cannot explain why Parler panicked when AWS shut them down, but if they'd had even a rudimentary and minimally competent IT department, they'd have been back up in 24-48 hours on another platform. (This is truly like Ford saying they won't sell you a truck - when there are many, many other trucks to choose from!)
Finally, Parler was not kicked off AWS for its political views - it wasn't even kicked off for the violent rhetoric posted on it... you're right - again - in your inference that those happen on FB & Twitter as well! The problem with Parler was that they weren't policing those types of (illegal) content, and removing them...
FB and Twitter do.
Finally, my guess as to why they dropped the lawsuit was that their suit had little chance of success. Your good friend Section 230 of the CDA protects them, so long as they move to remove illegal content when discovered, and respond quickly when reported.
Exactly what Perler was accused of NOT doing by AWS - which is why, to protect themselves and their other clients, AWS first warned, then threatened, and finally de-platformed Parler...
All the squealing by Parler was just their attempt to make AWS look bad - but, at least to the tech world, it actually made AWS look BETTER!