That would lead to consistent notation with x* and r* as you suggest, but we non-dimensionalize by theta_i given that it is not a function of time. theta_o is a function of time and thus both numerator and denominator would be changing with time which would not be good for non-dimensionalizing. The spatial Heisler chart does non-dimensionalize by theta_o, but we multiply the theta/theta_o read off of the spatial chart by the theta_o/theta_i from the centerline Heisler chart and this results in theta/theta_i - the same as theta*.
