For a while during the peak of OWS, I did what you suggested, but using Tor to snag some IP somewhere. When I'm done with my FB toy, I just stop playing with it - nothing tracks back to me, as long as I don't troll my friends' pages.
I don't have much use for ultra-security, but it's nice to know how to acquire it. Just cuz. Sure if the Feds wanna know, browsing encryption like SSL/TCL is relatively small bit-size for the keys (thanks to national security, cyphers are classified like missile guidance, and it's illegal to export algorithms that work too well for the NSA to hack).
There's other ways around this, of course. Not all encryption relies on a cypher like RSA, etc. Tor (the Onion network) works by nesting chains of IP's from around the world, so even if you're browsing http not https, it would be a monumental task to figure out who is on the other end of any exit node, even for the NSA (the Feds uses Tor too, for this very reason). Your browsing is in plain sight, but YOU are not - you could be anybody. There's other similar projects to Tor - JonDo springs to mind - but Tor is robust and under heavy development. It's also a snap to use and almost as fast as regular browsing.
Supporting Tor is one of the most important things a progressive Netizen can do to help oppressed folks in China, Iran, Pakistan, etc. get around their respective national firewalls. The more people who use Tor, the faster and more secure the network is. I keep a Tor exit node running on my entertainment machine just in case a Chinese dissident wants to read DU. 
With Tor, they can.
If everyone using Facebook would use Tor instead, we the people would PWN the Internet.
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