I want to be able to tweet my base URL, not my post URL.
When I tweet my post URL, my readers view the post and move on. If I could tweet the base URL for my site instead, they'd not only see the latest post but be able to scroll older posts too.
I'm a photographer and getting viewers to look at multiple images and stay on my site for longer is key for me since visual art is so personal.
I'd rather the link that went out in the tweet was just to http://www.richarddavisphotography.com and not to the specific post.