Theses are my thoughts on the question. I can't find an answer to "why not?". It there something I am missing, or are auto manufacturers simply too focussed on cars only?
The automotive industry has been developing internal combustion engines for many decades. They are now routinely capable of running for 20,000 miles service interval, which is a simple oil and filters change.
20,000 miles will be around 2000 litres of fuel, which is comparable to the oil required to heat a house in the UK for a year using an oil boiler.
Air source heat pumps are only just capable of offering cost savings to a UK household, compared to an oil-fired boiler, because of the inefficiency of the power stations and electricity grid in delivering electricity to the house, compared to burning the fuel locally. A local heat-pump gain of 4+ has to be multiplied by electricity generation and distribution inefficiency (around 0.5? Not sure).
The auto manufacturers' investment in internal combustion engines in under threat from electric vehicles. They have made the investment to mass-produce engines, and ought to welcome another possible use for much the same.
So, why don't the auto manufacturers develop an domestic air source heat pump based on an auto engine?
The water cooling system would be the house's central heating system. Auto cooling normally runs at 90C. Domestic heating systems normally run at no more than 70C for safety reasons, and often as low as 30C for thermodynamic efficiency reasons. Would this be a problem?
I don't know what fraction of a car's fuel is lost as heat via the exhaust pipe. In any case, some (large?) paer if this could be reclaimed via a heat-exchanger, as with a condenser boiler.
The rotary motion the engine generates could either directly run a compressor, or run a generator to provide electrical energy for the house with excess sold back to the electricity utility. Unlike solar panels, this energy would almost by definition be generated at times of maximum demand (in the UK, the coldest weather. In hot countries, the hottest weather, for cooling). So this would automatically be a benefit to utility companies and they might offer a good price even without the government forcing their hands.
An auto engine can provide a range of power levels, so the system could easily modulate its output to match demand.
I'd guess that an auto engine driving a heat pump, directly or indirectly, could have a heating efficiency of 2-3. Heat pump efficiency for driving a hot water central heating system is typically 3, so that lower figure allows for some losses. A modern boiler's efficiency is 0.85. I'm guessing that overall electricity utility plus heat pump is around 1.5
Annual servicing would be an oil and filter change. By using a larger oil supply and larger filters, it might be straightforward to push this to 2, even 3 years. Costs not a lot more than oil boiler servicing. Also a fixed installation should be a more benign environment than a moving vehicle.
I know that a petrol engine can also run on natural gas. Presumably a diesel could be modified to run on kerosene. If not, this would require a household without a gas supply to use diesel as heating fuel. Governments might worry about leakage of tax revenue from the heating oil tank into a car's fuel tank. However, in any case, electric cars are going to destroy that revenue in coming decades. (In the UK, farmers use low-tax "Red diesel" for tractors and heating. This fuel is dyed red so auto fuel tax evasion can be detected).