You are absolutely correct that we need one more postulate: I postulate that expanding civilizations destroy nonexpanding ones on contact. (They turn them into negentropy-source or computronium or whatever.) This suggests that we are in a relatively small part of the space-time continuum unoccupied by expanding civilizations.

But you are right, at this point I already postulated many things, so a straight application of the Anthropic Principle would be a cleaner solution to the Fermi Paradox than my roundabout ways. Honestly, in a longer exposition, like a top-level post, I wouldn't even have introduced the idea as a solution to the Fermi Paradox. But it does show that our observations can be compatible with the existence of many civilizations.

I believe that the valuable part of my idea is not the (yet another) solution to the Paradox, but the proposed 0-1 law itself. I would be very interested in a discussion about the theoretical feasibility of light-speed expansion. More generally, I am looking for a solution to the following problem: if a one optimizes a light-cone to achieve the biggest computational power possible, what will be the expansion speed of this computer? I am aware that this is not a completely specified problem, but I think it is specified well enough so that we can start thinking about it.