I was thinking of 5 to 10 units per day, per person (or household). I don't think you would do much mining with that.

Why not just give low income people a voucher / tax deduction equivalent to basic heating / power needs?

That way you don't subsidize people like me, who honestly don't need it.

Otherwise if nothing else you're incentivizing people into using their freebie electricity instead of gas for heating, if they've run out of freebie gas but not electricity.

Capitalism isn't perfect, but pricing goods according to supply and demand is kinda the thing the market does best, and if you think you'll do better you should think again. Nothing is perfect, but interfering with this part of capitalism is pretty much guaranteed to have unintended consequences.