If I self-host, for example, then I can hold on to my stuff until either I get a subpoena or the cops show up with a warrant. In the meantime, I can decide if I want to risk charges for destroying any evidence, I can call for lawyers, all these various actions I can take before my data gets handed over. Beats the hell out of getting an email to your backup account: "Your domain has been taken down at the request of law enforcement. Please have a nice day. Do not reply to this message."
How exactly does self-hosting protect you from the government taking down the domain? Unless you run your own domain registrar, the government can just change the DNS servers for your domain. That doesn't give them the data but it takes it off of the internet (as far as they're concerned; depending on how dynamic your IP is, it could be a nightmare for anyone to try to find via IP address or IP address range).
> companies like Google are more likely to just roll over
More likely than who?