It addresses reliability by shedding the customers who don't pay a premium for reliability first. Most of the time, that can solve the problem. It is, as you say, imperfect because it doesn't allow that premium to be used to fund investment in reliable generation.
What you're really talking about is demand response. It's been around a while in both commercial and residential settings.
It doesn't really address reliability to the extent that reliability depends on investments in distribution, transmission, generation, fuel to the generators, etc. If those aren't there, it doesn't matter if the user has opted into reliable (non-interruptable) power, because the power won't reliably be at the meter to begin with.