Bear in mind, exchange of any type = publicly traded, and LRM don't want that.
How public is public though? This forum is public and shares/bonds/contracts are trading here already.
Edit: LR has also indicated someone was working on an exchange at some point, so he's not totally against the idea.
From what I've pieced together, the contracts now look "legal" (although very difficult to valuate) and are clean. He's legally allowed to sell them to anyone. Once you own them, they are your property and you can sell them to someone else (within some limits so you don't draw attention to yourself as selling unregistered securities). However, running something that is an exchange (centralized place where people can trade contracts) requires more regulations. He doesn't want to get involved with that. Whether it's public or not doesn't matter, any centralized market is a regulatory liability for the operator. That's why it appears his lawyer is ok with someone else setting it up an exchange in a permissive jurisdiction. There is some regulatory liability placed on participants in the market, especially if you are a large holder of shares (selling unregistered securities), but that is kind of a stretch and might not be worth anyone from the SEC's time to look into.
Two things LRM contracts need, in order to have any value in the future, are a working exchange and enough information for people to value how much shares are really worth. Well, in theory, LRM only needs to have a way of accurately assigning value to shares (since that will allow direct, one-time, sales), the exchange is icing and will increase the value of the direct, one-time sales.
" Once you own them, they are your property and you can sell them to someone else (within some limits so you don't draw attention to yourself as selling unregistered securities)."
I don't think so, so what difference would it make what you do with your own property?