The stats do nothing outside of what is described on the OP. Generally we try to keep it as simplistic as possible (usually that works well until we start rolling formulas around) but it's mostly in check to compare power levels and prevent godmoding. Quantifying things like willpower and intelligence leaves up a lot for interpretation. 

The problem with nightmare having no statistical resistance check is simple. If you're fighting one giant monster with a team of 3-4 people, one of your allies distracts them and Charles casts Nightmare, then your team can basically kill without any risk the moment it kicks in, which wouldn't be very interesting more than once. Support abilities are some of the easiest to go OP with ;p