git practically already has this with the --depth option to git-clone. The only thing that it's missing is the ability to enforce storing the last single commit.
I'm sure that you could probably build the system that you are describing on top of git, but you would still run into problems with large files and local commits, even if it was just "commits since last pull/push."
Yes, git almost has the shallow repository done. It's even in the article, and that "almost" means it's almost trouble free, but will catch everybody off-guard once in a while.
The other part about the simplified evolution graph is completely missing. I don't think one can solve that without completely rewriting the protocol.
I'm sure that you could probably build the system that you are describing on top of git, but you would still run into problems with large files and local commits, even if it was just "commits since last pull/push."