Correct. But integrating over multiple pulses, and using the latest Tx and Rx modules, sensitivity is not the problem anymore. Radars can easily see every damn bumblebee in a 100km radius. The problem is filtering data, so that processing and/or the user is not overloaded. For example, if you track every single bird with a radar that has a 100km radius, you will not be able to see anything on the operator screen other than birds.
Doppler is easy to filter on early in the processing stage. Meaning that if you can detect the aircraft, you can still separate it from all other bumblee like objects. Clutter tends not to move that fast.