Why do we measure \$I_{ds}\$ for CMOS instead of \$I_{sd}\$?
The standard way to write current across a MOS seems to be along the
  \$I_{ds}\$, i.e. from drain to source.


Let's pick at that statement: -


Current is not "across" something but voltage is
Current is through something but voltage isn't
Current is best defined as into a node or from a node


Given the above, EEs talk about \$I_{D}\$ or \$I_{S}\$ but not \$I_{DS}\$


  but would it not be more natural to think of current as flowing from
  the source to the drain?


If the current is the same then it doesn't matter but it's not the same for (say) a bipolar transistor because the base takes current and \$I_{E}\$ is not the same as \$I_{C}\$.

So should we change this well formulated way of stating things specifically for MOS devices? No we shouldn't.