Do you think an installation with a CoP of >1 gives you free energy or something? It does not. An installation with a CoP of 2 still uses energy, and twice as much for the same heat demand as an installation with a CoP of 4. A CoP of 1 would be equivalent to a resistive electric heater, which is generally considered to be the worst way to heat a house. Cost wise with the energy prices in my area you need a CoP of between 2.5 and 3 to break even in energy costs, and with the grid here still being largely dependent on coal and gas in the winter you’d need a CoP of around 2 to be positive in CO2 footprint. Most heat pumps can easily reach that CoP, when used sensibly.

Tanks with thermal gradients also do not matter for CoP. What matters is the difference between the hot side and the cold side. If you have to heat something up to a higher temperature, that efficiency is lost, regardless of what happens with the heat afterwards.

The video also shows the exact opposite of what you claim. You can clearly see that the power required to run the heater goes up as the temperature increases. And yes, topping up requires relatively low amount of power compared to a cold start, but that’s because it doesn’t have to add much heat energy to the tank, not because of a difference in efficiency during top-up.

I’m also not saying you need a heat pump for every single tap, I’m just saying that relying on one single heat pump for all your heating and cooling needs in your house is a stupid idea. It of course makes sense to have one heater for all hot water taps in your house. But it does not make sense to run your heating and dryer on the same heat pump, unless you like wasting a lot of electricity.

You also mentioned per-device inefficiencies, but it’s actually the opposite. Heat pumps are at their most efficient when properly sized for the installation. If you have only a single unit then it has to be sized for the peak demands you might need, and it will not run at peak efficiency in the summer when it just has to power your dryer. Having a dedicated heat pump inside the dryer that is properly sized for exactly the heat output the dryer needs is much more efficient. And that is even ignoring inefficiencies behind heat distribution you’d have with a centralised setup.