Searchlights work by focusing light from a source to infinity. Physics dictates that small light sources focus better. Getting searchlight-level brightness from an LED source will require an LED array, which will be too big to focus effectively.
LEDs make excellent floodlights, but if you want reach, xenon discharge lamps are still the best option.
However, the diameter of each LED optic would need to at least equal the diameter of the single optic used for a point source light. The result would be an enormous searchlight with a very broad beam.
I can't find any solid information on the quantitative light output of the AN/TVS-3, but xenon arc lamps typically produce 30 lumens per watt. Therefore, the 20KW AN/TVS-3 should produce around 600,000 lumens.
Readily available high-power LEDs are capable of 1700 lumens, so equaling the AN/TVS-3 would take--as a very rough ballpark that does not take into account the different light distribution between LEDs and discharge lamps--350 LEDs and optics. The AN/TVS-3 uses 30" optics, so those optics would also need to be at least 30" in diameter.
350 30" optics is a lot more like a wall of light than a searchlight. Aiming that many separate optics would also be a nightmare.
https://en.wikipedia.org/wiki/Luminous_efficacy
What I'm not sure of is if the lumins/watt rating is given for the light output or the power input.
The input power rating is 450 Amps * 200 Volts * 1.732 = 155880 electrical watts. That's nearly 7.75 times as much electrical power as light output. That makes sense since the peak efficiency is about 7.3 for a xenon arc lamp.
I probably am missing something about optics though.
Bigger optics = less beam divergence = more useful range.
This is a function of the diffraction limit[0] and is a property of physics.
If you want to match the beam divergence of a 30" optical system, you have to use 30" optics; there are no shortcuts.
[0] https://www.edmundoptics.com/knowledge-center/application-no...
I can, however, imagine that a multi source system would require in-phase light sources to kind of mimic a phased-array receiver on the send side.
XKCD explainer here: https://what-if.xkcd.com/145/