Why not produce household electricity with natural gas generator?
Considering the investment for the generator, its maintenance, etc, the only way this would be viable would be to use cogeneration. This means using the waste heat from the generator to heat your home in the winter. In this case, even if the electrical generator efficiency is only 20%, global efficiency will be close to 100% since you'd use the heat.

However this isn't very practical as the generator would only run when heating is required, which may not be at the same moment than you need electricity. 

Note that the gas use of the generator you quote is most likely specified at full output power. If you only use a small part of the 10kW power, efficiency will drop a lot. If you don't use any power, the engine will idle and consume gas for nothing.

Also, an internal combustion engine doesn't last that many hours...

If your air conditioning bill hurts, first thing is to add insulation and shade the windows, then you can use solar panels to power your A/C for example. And it doesn't use any gas...