Is the government offering to provide Internet services to you? You're comparing apples and oranges.
A government still can, and will, seize domains, block sites, and issue takedowns and warrants on content to Google. Suppose I own xyzzy.com, set up to use Google Apps to handle mail and serve some web pages. Just like if I was hosting at home or in a colo somewhere, the government can still come in and demand the data. In fact, the biggest difference is that companies like Google are more likely to just roll over--see the stories about cell carriers just handing over tons of information just because law enforcement said please.
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).
A government still can, and will, seize domains, block sites, and issue takedowns and warrants on content to Google. Suppose I own xyzzy.com, set up to use Google Apps to handle mail and serve some web pages. Just like if I was hosting at home or in a colo somewhere, the government can still come in and demand the data. In fact, the biggest difference is that companies like Google are more likely to just roll over--see the stories about cell carriers just handing over tons of information just because law enforcement said please.