But many things we might simulate with computers, like the weather, the economy, or existential risk, are full of power law distributions that might not have a convergent expected value.

Some of those power laws have to break down. If you find a storm of 10^30 J, it isn't Terrestrial weather any more. Similarly, if we ever had 10000% growth in one year, that's probably because we hit the singularity and all bets are off.

The models may incorporate those divergences, but only because they're wrong.