If airborne radar exists which can track fast moving targets from a fast moving platform, and sort out everything about everyones' positions and vectors to within a gnat's whisker, why can't ATC radar do the same? In other words, why does ATC radar need the aircraft to tell it what altitude it's at? I would have thought radar could be much more accurate than steam-driven altimeters anyway.
Mechanically scanned radar heads suffer from relatively poor bearing discrimination, plus can only normally check azimuth or elevation separately; normally two synchronised heads are required to acquire azimuth and elevation data together.
The total bearing accuracy is typically about 1 degree at best, maybe worse than this in elevation, due largely to beam width limits. A target at 5000ft and 30 miles from the radar head has an elevation angle of less than 2 degrees, so sufficiently accurate height data is simply impossible to derive from conventional radar at realistic operating ranges.
It is possible to use radar to get better 3D pictures of close-in airspace using military phased, steerable array technology, but still not to the altitude accuracy needed to control lots of CAT at say 30 to 50 miles range. At the moment the civil radar heads used by ATC are a little bit more antiquated than the best military kit.