For your old appliances you still pay the same on average. A fixed price contract isn't cheaper, it just smooths prices into a long-term average. And many of the changes can be done manually. On your old dishwasher or washing machine you decide when they start, and most of them even already have buttons to start with a fixed-time delay. Instead of starting them at the end of day you can just start them when the wind is strong or the sun is shining, or watch the price feed. You even get to feel smart for saving money
I agree on the popularity, but you'd absolutely see an effect even without anyone buying new appliances
Years isn't that long.
The aim is net zero by 2050, lifespan of a fridge-freezer is about 10 years. Even assuming designing a system and putting it in place took 5 years, that's still enough time to have most appliances on it by 2040.
Given the current energy prices, it probably even makes sense to replace appliances sooner than their normal lifetime. My fridge-freezer is only 5 years old, but if it broke today and cost more than ~£150 to repair, I'd end up saving money by replacing it.
Each year is a significant fraction of a government mandate though.
And in the meantime it would be very unpopular for people who can't just afford to renew their otherwise fully functional appliances.