A random delay is also a tell, though. An obvious move shouldn't take 15 seconds, but if that's what the random delay for that move is, that looks suspicious. A more difficult move shouldn't take only 3 seconds, but if that's what the random delay for that move is, that also looks suspicious.
Definitely, random time is adding no correlation where it would count. Move time is an easily captured psychometric observation, the clever bit is that it’s intermingled with automated chess analysis.
Feels like there could be a lot of surprising inferences to think about here … just a few quick thoughts - how long does someone pause after a blunder, how does one react to unpredictable moves. Can definitely imagine AI being of significant utility here.
