I don't think this is a 'possibility'. Empirical observation indicates clearly that everything is not "random". That's not to say that the opposite is clearly so — it isn't. But it is clear that many things exhibit some degree of order. So I dismiss this 'possibility'.
Indeed, it may be so. Or it may not. I don't think anyone will have done the research to answer this question, so it looks like you'll have to do it for yourself. There's a lot of work to do, though, To investigate so many "configurations", to see which of them conform to your simplicity criterion, and how many don't. This 'possibility' can be confirmed, or denied, but it's a lot of work. Good luck with that!
To investigate this one, you'll need to know the probability of every configuration you look at. You'd better hope none of them are the sort of problem we've been discussing, where the probabilities are not calculable. I agree that the world seems not to confirm this 'possibility', and I would add that it would be very odd if all 'configurations' had exactly the same probability of occurrence. Very odd. That would make them all random, wouldn't it? Or would it?
I'm not 100% clear on what 'configurations' are, but this one seems quite credible to me. I imagine there are many configurations, very many, of all different 'shapes' and 'sizes'. Some will be simple, but many will surely feature some complexity? The universe is not an especially simple place, after all, and I'm guessing that the nature of these 'configurations' will reflect, in the most approximate way, this feature of the universe...
[As above, this one might be answerable, after a great deal of work. But I wonder if the answer is worth all the work?]