Daikin (and presumably others, but they're the ones we went with) do have integrated tanks/heatpump internal units. It might be worth having a think about your actual needs and it may be that there is a solution.
My experience with electric hot water taps is that they've been universally awful and only a last resort, but equally the state of the art may have moved on since I last looked!
I'm currently investigating options for kitchen sinks and such. It feels quite silly to have a long length of pipe leading from a central source for a small amount of warm water to wash my hands.
There's a limit: you can fill a medium saucepan with boiling water, but large/industrial-kitchen pans will exhaust the boiling water and you'll need to wait for the next batch.
It's fine for general household use.