Radar does work, there's just a trade-off between frequency and resolution. LIDAR is way up in the near-optical regime, so it has very poor penetration but the resolution is so high that you can see the small gaps in the canopy. Importantly, you can also do fancy signal processing with the reflectance and multiband stuff to distinguish man-made objects from foilage. That's uncommon in the archaeology world (unless using data where that's already been done), but the military and commercial people take full advantage.