It's already implemented, it's just not derived. Indeed there is already an arbitrary 'area' over which the linear measurement for rainfall is captured, mass and volume are trivial to derive from this - we just don't.
In fact I have built a small weather station at my house, which is monitored/logged by an ATMEL device (think Arduino but more sophisticated), it measures rainfall by mass, then derives the reverse linear measurement for reporting. Similarly, the anemometer measures in RPM, and direction is sourced from a vane, both are then used to derive wind velocity.
I'll have to take your word for it. The science behind it is beyond my level of comprehension. But if your converting back to a linear measure, what's the point? Stick with the good old rain (or dust, most of the time) gauge!