Isn't it a bit odd that football allows the ball to be advanced on a fumble?
Yes, it IS odd, because football is directly descended from Rugby.
In Rugby it is illegal to fumble the football forward. It's a penalty called a "Knock-On".
As such, if American Football wants to be true to the original intent of Rugby, then the rule should state that the ball cannot be advanced by the offense, should the offense fumble and recover. Today's play would be resolved by placing the line of scrimmage at the point of the fumble, not the recovery.
Of course, if the Defense recovers, they may advance the ball.