what's wrong with that picture? Think about the strain of PULLING the board tightly against the fence for one thing. You can't even see the interface between the boards and the fence to insure an even cut. If you have the fence on the right like you are supposed to, you can be sure there's no gap between the board and the fence, PLUS you can easily PUSH the board into it's proper position flush against the fence more easily than you can PULL it. Besides, how on earth can you deal with wide stock like plywood, MDF, etc. You'll have to have "mutant" arms to reach the far side of the stock! :)
Sorry George, what you are suggesting is awkward and can easily result in improperly cut boards. Try the "normal" way; you might like it.
Dave