First of all, they do not take advantage of the fact that the speed of light furnishes a unique and universal relation between the standard of time and the standard of length.
Second, for an accelerated reference system the (pseudo) gravitational frequency shift frustrates the synchronization of clocks indicating proper time.
Third, the pseudo gravitational redshift changes the wavelength of light and hence brings about discrepancies between the atomic standard of length based on a fixed number of wavelengths of Krypton 86 (more recently, of iodine stabilized He-Ne laser light) and the atomic standard based on a fixed number of platinum atoms (rigid platinum-iridium meter stick in Paris).
Last, but not least, there are regions which simply don't lend themselves to being probed by rigid bodies, if for no other reason than that the assumed rigidity of material meter rods loses its meaning when the acceleration becomes high enough.
The methods of Doppler radar and pulse radar do not suffer from any of these disadvantages. Moreover, it is possible to formulate the entire kinematics of special relativity in terms of the methods of radar.