Tabby, I've been doing a lot of research lately for a concrete wall my son wants to build in Phoenix. I remember seeing a site where a couple built a concrete block shed but darn it, I can't find it now!
I can't think of any reason why you "should not" build one, as long as you take the necessary steps to lay a good footer with vertical rebar for reinforcement, etc. they're practically indestructible and last forever! The "split face blocks" are more expensive but obviously have more aesthetic appeal and you're right, they wouldn't need painting.
With the proper tools and planning you shouldn't have any problem building it yourself. Good luck!