What do you think of Max Tegmark's answer, that it's because universes with every possible (i.e., non-contradictory) set of laws of physics exist and we happen to be in one with electromagnetic dynamics derived from Maxwell's Lagrangian?

I think Tegmark's idea is either tautological or preposterous, depending on what he means by exist. If exist means ‘exist in an abstract, mathematical sense’ (as it does in the sentence There exist infinitely many prime numbers) then it's tautological, and if it means ‘physically exist in this particular universe (i.e., the set of everything that can interact or have interacted with us, or interact or have interacted with something that can interact or have interacted with us, etc.)’ (as it does in the sentence Santa does not exist), it's preposterous. The last chapter in Good and Real by Gary Drescher elaborates on this.

Once again, we badly need different words for ‘be mathematically possible’ and ‘be part of this universe’.