Fast boot is cool, and since there is also a "restart" option that shuts the phone down properly, I'm tempted to leave this option enabled should I ever want to use it, however in the settings menu, the fact boot option says "disable to use some market apps" and I wonder what functionality I am losing by leaving it turned on.
I honestly can't think of a reason I would hibernate my phone. The only time I ever turn it off is to reboot it, so if there is some downside to the fast boot option, I'll leave it off, even if it is a neat party trick.
Android Guru here. I initially had the same thoughts on "whats the point" regarding fast boot. I guess there are times when you might want to shut off your phone for battery reasons. Still, hibernating does use a tiny bit of power (compared to actually being off) so I don't think it's worth it.
The most likely reason for the market apps warning, though worded pretty poorly, is that Android fires broadcast intents that many apps listen for upon the phone finishing a boot. This hibernate mode probably doesn't fire that intent, as the phone didn't truly boot.
Thus, any app that needs to do something based off of the phone first turning on probably won't do it.