Wow, thanks for all the suggestions.
Part of the reason I thought this would be a really good idea, is that a thief would have to either make a cut in a really tight place (and his cutters might not fit), or he'd have to saw through the seatpost, or take out the BB. So it seems really secure.
Also, it would be almost invisible, and I was looking forward to having a pretty bike.
But you're right that this would provide zero deterrence, and that somebody who loosened the bolt but found that the seatpost was invisibly prevented from coming out of the seat tube, might resort to more forceful means rather than giving up. And that would be bad.
Also, I didn't know that modern seatposts were solid at the top. That definitely makes this solution a lot less elegant.
I guess I'll end up doing what everybody else does, with the locking/gunk-filled bolts. Or maybe I'll try a Torx bolt...that way only Macintosh repairmen will be able to get it off.
Thanks again!