There's already something called time-of-use metering, which is like what you're suggesting but based on long-term trends rather than a spot price.
Right now it's only cost-effective with large loads, and only economical if it's largely automated.
(By point of comparison, most people already can't be bothered to switch off a 100W room light when they leave. That means we just don't GAF about saving pennies per hour if it means we have to push a button every so often).
However, seeing how heating and cooling are the only residential loads that are really worth worrying about, and both can typically be advanced or deferred by an hour or so without any problems, you could probably solve 90% of the problem by smartening up a handful of appliances in each home.
Industrial users can often do similar things. A cold storage facility, for example, could do most of it's cooling when power is cheap and then coast through the expensive periods. And they use enough electricity to pay someone (or buy an automated system) to handle it for them.
Once you solve heating and cooling, everything other than cooking (basically lighting and entertainment) is getting more and more efficient every year. And most people don't cook enough to make that a significant load.