Model II system desks do pop up from time to time, but they really cannot be shipped so they are a regional item which makes them rare. Also, a lot of people have them and don't know what they are so that makes them rare as well. I once bought a Model II system from quite a distance away and I just happened to ask the seller, "Was this computer found on a desk?" "Why, yes", they replied. I went ahead and described the desk and it matched the Model II system desk perfectly. Then they proceed to tell me "I gave that away to my relative. I did not know it went with the computer."
Ouch!
I also have acquired a few Model II system desks over time, but a lesser number of Model I system desks. It does seem like the Model I desk is rarer, which on the surface seems strange. It's probably due to it's weaker construction. Most have bowed tops due to the thin particle board used. The Model II desk top is a serious table top, and while it is particle board, it is about twice as thick. The Model II system desk also has a center support strut and much beefier steel structure.