I'd definitely spend one or two thousand gold on a statue that didn't do anything but tell everyone who came into the region how cool I was. What else are rich dukes supposed to do with all their cash?
Actually, it would be pretty cool if you could erect statues to other people. "My favorite knight/my mentor/my lover/whatever has fallen in battle, I shall build a statue for him." "I shall prove I love you by building a statue in your honor! It shall be almost as beautiful as you are!"
Didn't Tom say that you'd eventually be able to build all sorts of buildings with different effects when the New Estate system was finished? If they actually have in-game effect, maybe they should be part of that.