I was not considering direct drive hydropower, my comment is about having inverters, which stop generators over loading even for a very short time.
There will, of course, almost certainly be a lot of moaning on the part of people who believe that they should have the right to decide when all of their appliances etc. operate
This is a major problem, we want the incentive to use power when there is plenty, but if we had two supplies, there would be those who would have some method to swap between the two supplies.
We have already seen this with immersion heaters, where people have two, one connected to off-peak and one connected to peak. There are two schools of thought, one if one is willing to pay more, why should they not use peak to heat water, the other is, the whole reason for the off-peak, is to reduce peak use.
The power and lighting supplies in the early days of supplying power, included a legal bit where if you were caught using a lighting supply for power you could end up in court, but we still had these.
Even today
OK, for use down under, but we would soon see adaptors for UK sockets, likely meaning no earth.
I believe the French had a problem with Smart meters, unlike us, the French charged different rates depending on supply size, which could go down to 16 amps. With a 16 amp fuse, a short overload to 20 amps was not a problem, but with the smart meter, it sensed the over current and opened the breaker, so was tripping at 20 amps even for a short time, so the user needed to pay more for an uprated supply.
To use a twin supply, the 24/7 supply would need a current limit to stop people simply swapping supply when there is a shortage of power.
There would be nothing to stop having electric showers and the like on a switchable supply, but I would be rather upset if lathered up with soap when the power failed.