One of the predictions generated by the mathematical universe hypothesis is that our universe is maximally general structure, subject to anthropic constraints. Are there any obvious counterexamples?

Mathematical universe hypothesis. So, for example, it seems like Tegmark's MUH should predict a varying fine structure constant, so long as it doesn't vary so much that it would interfere with the existence of life. It predicts this varying constant because a mathematical universe where this dimensionless constant varies is a more 'general' mathematical structure, and hence more typical, than one with a fixed fine structure constant. Are there any examples of how the universe could have been more structurally complex, but in fact is not, and hence could have been more 'general', in a way that wouldn't obviously interfere with the existence of life?