Why fossil fuels make fuel poverty worse

There’s been coverage in the Financial Times about fuel poverty.  People are saying that the UK government will have to cut back on its renewables ambitions.
This seems to be bad economics quite apart from considerations of climate change.
The argument is below.  However, it doesn’t appear in the press coverage of the issue so it is probably wrong.
1. Energy conservation and the generation of heat and power from solar, wind and nuclear sources are characterised by high capital cost and low or zero fuel costs.  Their cost fluctuates broadly with the cost of capital.
2. In contrast, the cost of conventional energy sources fluctuates with the cost of fossil fuels.
3. With time, technology gets relatively cheaper.  In contrast, fossil fuels will get relatively more expensive as they become scarcer.  Thus, while technology will get cheaper compared to people’s incomes, the cost of fossil fuels will grow faster than household income.
From (1), (2) and (3) we can see that as time goes on, a fossil fuel economy will have more people trapped in fuel poverty than one which has invested in energy conservation, renewables and nuclear.
There is another argument for the case of people in difficulties with their fuel bills
4. In the case of energy conservation and solar and wind power, the main cost is the servicing of finance.  So if people get into difficulties, as a matter of social policy financing can be restructured or resheduled, giving some flexibility to the end consumers.  Because the technology doesn’t depend on the ongoing supply of fuel, this can happen without interrupting the supply of energy.
5. However, there is no equivalent flexibility in the case of fossil fuels. The fuel has to be paid for, especially if it to be imported from another country.
From (4) and (5) we can conclude that an economy of energy conservation and renewables has more flexibility for helping people stuck in fuel poverty than a fossil fuel economy.

It would be good to know if this argument is right or wrong.

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