This is a governance failure: for letting prices get out of control, for allowing poverty so bad that _people cannot heat their homes_, and then for allowing utilities to shut off people's utilities like this.
It doesn't have to be that way: on that last point for example, in Ontario, Canada, there's a law that says that a utility cannot shut off a house's electricity or gas during the winter for non-payment. It doesn't matter how far behind you get on your bills, it's illegal to shut it off. This would, I think, make pre-payment meters illegal here, and this probably explains why I've never heard of them being a thing.
By your admission it is not illegal to turn the electricity of during summer, but presumably people have to cook there too?
The solution is not to let people use electricity without payment, because that will be abused. Have the bills be paid directly for those on unemployment if you want, raise the benefits to match if you want, but a system where there is nothing that effectively stops you from not paying is going to result it bad outcomes for everyone.
Welfare is essentially a subsidy for crap wages. U either pay them a proper wage (surplus value) or u get taxed for govt services.