The kiwifarms saga was a really interesting deep dive in to how fragile the internet is. In the end they were able to get back online but it takes a monumental amount of work, redundancies, and relationships with infrastructure companies.
Currently the main weak point is ISPs. It’s not impossible to find hosts who will ignore complaints, but ISPs in the middle of the route can start disrupting traffic and causing connectivity issues for people in certain areas.
In general though it does seem like there is a need for more infrastructure hosts who stick to enforcing the law and just ignore the twitter drama. Epik domains and Terrahost seem to be leading this category.
Depends on your needs, but it is fairly simple to buy a domain-name and manage the dns-servers and hosting of web-server (and I guess e-mail) yourself.
If you have a A/AAAA-record in your top TLD pointing directly to your nameservers you do not depend on anyone but the root servers and TLD-servers to be available (in regards to DNS). Now, you just need to find a TLD that is not managed by one of the big ones, but that should be fairly easy.
At the end of the day, it's all about the tyranny of the middlebox.
Let's say you get banned (somehow) by backbone, but you have one other middlebox willing to proxy you.
You're still visible! You're just behind that middlebox's routing. In fact, if you enplace yourself within an AS as an Authoritative DNS provider, suddenly, you da boss. I can make (from my network's point of view) facebook.com resolve anywhere I want for requests coming from within it. Now. If I had a channel to receive updates on the address of a service the big guys were trying to crush, say, TPB, my resplver can be updated to resolve that without honoring upstream.
This was actually how DNS started. It was just lists of host names to IP's/ARPANet addresses.
The challenge is always figuring out how to distribute notice of the changes.
I wonder what it would take to host a website and be reasonably outside the blast radius of any of the parties you named as controlling the internet.