Because you'd also like to know the phase of the waves. If you get unlucky and get just DC offset of the waves (think of it as the 0 crossing of a sine wave) then you've no idea what the phase is. The peak could be before the 0 crossing and the minimum could be afterwards, or it could be the opposite (pi offset in phase). Granted, this is unlikely to occur, you're much more likely to not run into these scenarios. Ideally, you want 4 pieces of data per wave, the 0 crossings and the max/min, for each wave. From that you can get the amplitude and the phase for certain (again, luck is involved)
Luck isn't involved as long as you can ensure your sampling noise is uncorrelated with the incoming wave, either by direct insertion of dither or characterization of environmental noise. Regardless, your point still stands, just a fun tidbit.
Can you not make a coherent quadrature detector? I was under the impression that those were pretty common in optical communication systems. Edit: nevermind, 230GHz, so millimeter wave but mixers and oscillators exist at that frequency, are the noise figures just too high to use?