It's not latency free to act on price changes. If they spike while people are asleep, what do you expect would happen? And would people get a notification everytime the price changed at all. The logistics are hard.
Minute by minute pricing is not crazy to expect and integration with HVAC, battery systems, and inverters isn’t crazy to expect to occur.
Now every device in your home knows the price. For this to work, everyone must get the same price across the whole grid, and there must be sufficient grid capacity for energy to flow freely which isn't always the case. It will also cause issues with some very old (ie. 60+ year old) clocks with mechanical timers.
All of these issues can be fixed by updating the formula:
price_per_kwh = tan(min(max((-60 + system_frequency + published_offset) * 1000, -pi/2), pi/2))
The published_offset would be unique to each district and adjusted from time to time to keep old clocks working properly, and sometimes to deal with limited transfer properties of the grid...
But the neat thing is that even if you don't take into account the published_offset, you still make nearly optimal economic decisions.
People will choose it based on claims in the shop like "Smart timing cuts energy bills by 25% on average!".
It only takes a smallish percentage of demand to be reactive like that and really big price swings won't really happen.
Somewhere they'll still be grandad manually putting the dishwasher on at a cheap hour or turning the hot tub off whenever he sees the price is high, but I expect most to be automatic.