We don't need an unbounded utility function to demonstrate Pascal's Mugging. Plain old large numbers like 10^100 are enough.

The scale is arbitrary. If your utility function is designed such that utility for common scenario are not very small compared to the maximum utility then you wouldn't have Pascal's Muggings.

It seems reasonable for utility to be linear in things we care about, e.g. human lives.

Does anybody really have linear preferences in anything? This seems at odds with empirical evidence.