Cogeneration is a good idea in many situations. The 1,000 watt
units that you mention would work OK for some applications,
It would work to keep the electric furnace fan motor running to heat
the house, power some compact flourescent lights, maybe even a TV,
during a multi-hour or multi-day power failure.
In reality, those 1000 watts would be wired such that the furnace fan
is always (and only) powered by that source during the heating season,
with the co-generated head used to heat the house. Combine that with
a variable-speed electronically commutated furnace motor and you've
got a great heating solution during spring and fall for a good chunk
of the US and all of Canada. Even if you never experience a power
failure in the winter, a co-generation unit like that could
theoretically be cost-neutral (ie no more expensive to run) vs a
conventional furnace.
but when we start talking about electric water heaters, electric
ovens and so forth
During a failure of grid power, we are not talking about a power
solution that keeps absolutely everything running.
The bare essential thing that must keep running to maintain minimal
disturbance to your lifestyle (if not survival) as well as to prevent
dammage to the home itself is the furnace fan. Everything else
becomes of minimal importance in that situation.
Besides, you will still have hot water if you have NG water heater.
people will probably still use a generator when there isn't
power.
The motivation to go out and buy a generator, let alone use one if you
already have one, would be significantly reduced during even a
multi-day power failure if your furnace fan was still operable and
your house was being heated normally during a power outage.
One of my relatives has a natural gas fired stove (looks like a
wood burning stove) and it seems to work just fine without any
sort of fan.
It's not going to heat the whole house during a multi-day power
failure during the winter.
That is probably the best solution if the big concern is
heating and cooking.
Having a warm place to sleep at night is the biggest concern during a
multi-day power failure in the winter. That, and to prevent your
pipes from freezing and real dammage setting in.
You can always drive around for take-out food, eat at a restaurant,
etc. But your SOL if your house gets cold.