Graybeard, the signal path is not quite that simple. There is a gadget called a circulator in there which protects the receiver front end from the transmitted signal and routes the majority of the received signal from the antenna to the receiver front end. The circulator is not perfect. 40 dB is good. 50 dB is darned good. But it plus an electronically switched attenuator can protect even fragile 1N34 diode front ends let alone the nice schotkey diode front ends we used in the 70s. That leakage signal is a VERY nice BIT feature. It's strength is "more or less" constant. You can certainly tell if the transmitter failed or if the front end packed it in. Both cases mean too little signal received. If the antenna has a physical fault to it that disconnects the waveguide that results in WAY too much signal leaking around the circulator. (It bips out of the transmitter through the TX path on the circulator to the open ended waveguide. Most of the signal is reflected back and takes the RX path to the radar set's front end.) So you have a tremendous amount of nearly free BIT. Similar BIT features on the antenna mount can handle aiming issues neatly. It's a feedback positioner and it is pretty obvious to the pointing software that it's not getting position feedback when it commands motion.
That handles a large range of the possible errors. If the temperature of the circulator is monitored and a calibration for it exists you should be able to detect even modest transmitter or receiver degradations, say half power or so.
I remember in the era that would have been designed that at least the Navy was frantic about having good BIT features on things like the S3A sonobuoy receiver. I'd expect the FAA to be at least as diligent. But, then, maybe not.