Capital cost would kill it with those units in a domestic dwelling.
Back in the late 70s a chap at the alternative energy place in Wales ran
a morris minor engine and generator with full heat recovery from exhaust
and coolant until someone ran it dry while he was on holiday. Later the
calor totem was shown on tv, it was a fiat 127 engine running an
asynchronous generator Quite a few were sold but engine life was the
problem and again they were too powerful for a single home, I know the
firm I occasionally worked for came across one running a hotel in Scotland.
I helped with installing a marinised Petter diesel with heat recovery
for a remote classroom and the fuel cost just about matched the value
of electricity produced but I know we could beat that seriously now with
a permanent magnet genset and inverter.
Then there were the couple of different Stirling engined units which
Briish Gas trialled and one of which was due to be put into a few homes
in Manchester but this was aborted. The Stirling ones should have had
similar (longer than internal combustion engines) life to heat pumps as
the units were similarly hermetically sealed, like a fridge, but only
gave out 1kW of electricity when run.
Now with the demand for EV charging I suspect the balance of heat to
electric power is better suited to a single user. Also engines are much
longer lived now too plus the modern electronics in inverters as used
for solar panels make it attractive to run an engine at its most
economical speed for the demand and rectify the ac and chop it back to
synchronous ac for the house.
Personally I would like to try this with the engine and permanent magnet
motor from a Honda civic whose NIMH battery pack had failed and caused
the car to be scrapped.
Not sure how one would get round the Gassafe requirements for
connecting to the main though plus I cannot afford an EV to make it
worthwhile.