Don't know where you get the 10KW figure STBYRUD, but the WXR-700X is 150 watts peak power, typical 1 microsecond pulse width, 180 to 1440 PRF, pulse repetition frequency. You can do the math to see it's less than one watt average power.
Here's the spec from Collins on the WXR-2100 Multi-Scan Weather Radar:
Transmitter
PRF 180 (up to 3,000) pp/s
Pulse widths 1 to 25 microseconds
Frequency (direct 9.33 GHz digital synthesis)
Peak power 150 watts nom
SPECIFICATIONS SUBJECT TO CHANGE WITHOUT NOTICE
3000x25=75000 microseconds. Divide by a million, times 150 = 12.5 watts average radiated power, max.
OK, I'll concede the 12 seconds to get to 80 knots, but I doubt it takes that long for alerts to be active. If true, it's no doubt worst case. Automatic antenna calibration is four seconds; the rest is solid state, and the first active sweep will identify doppler shifts.
I still can't fathom why Boeing would change from oil pressure plus transponder to TLA (alone?) One less wire?
GB