Having a 10000 watt or even 20000 watt whole house generator to power a house is the equivalent of having a semi truck in the driveway to pick up milk. Now that is when you have an inverter with a battery bank. Average power use in a big house is roughly 500Whr/ht to 1kWr/hr. You do need that huge generator for the start up load or to run large loads simultaneously. The dedicated loads electrical panel with the critical stuff on it is a better solution. I have a 4500 watt generator at home for charging up batteries in a long outage when the panels can't keep up. It would be powerful enough  to run the heat pump, furnace fan and water pump on its own. I would not run it continuously even if I had no battery back up as the idling fuel use would be too much. Idling is where those inverter generators come in handy as they can idle down to match the load on them while maintaining perfect power then ramp up fast when something bigger comes on. Usually an inverter generator is not ideal for battery charging since you are pushing it heavy the whole time so the fuel saving qualities are not used.