It's complex (or I'm not being very clear!)
Premise:
Everybody who lives in Council Tax Bands A-D gets to use 200 at £1 each
Everybody who lives in Council Tax Bands E-H gets to use 200 at £2 each
This is fair because somebody living in a house in a higher band must have a bigger property/higher income
Household A,
Band C, Three bedroom semi. Has a new boiler and additional insulation fitted in the last 5 years because the property is 30+ years old.
Rent £500, Council Tax £100, Pays £200. Total = £800
Household B,
Band G because they're been housed in a place with fewer bedrooms than A somewhere else in the country because that's the only area they are eligible for housing. Property is smaller, newer but doesn't have a combi boiler or anything more than the legal minimum insulation. Housing Association will not be replacing anything for around 10 years.
Rent £650, Council Tax £240, Pays £400. Total = £1290
Income of Household A = £2500/pcm
Income of Household B = £1900/pcm
(amounts chosen because they're above the earnings level for UC in the case of both households)
They both have the same appliances and use exactly the same amount of energy. Energy is down as a generic 200 units of something at £1/2 for ease.
Household A also received £400 Council Tax support because of their banding. Household B didn't. And now A's fuel costs are lower as well because they live in a place that has a lower banding (and in a cheaper area). It's not B's fault the only place they can live is deemed to be of greater value, they had to take what they were given and were eligible for (and they are grateful for it, the alternative was homelessness, after all), but they have to pay more in rent, council tax and energy bills as a result.
Same way C and D could live in exactly the same band property in the same town, but D doesn't own theirs, so has no influence upon the landlord to fit insulation, double glazing or a combi boiler, but they do have to buy and run a dehumidifer to prevent damp as it's a condition of their tenancy. C uses 200 at £1 = £200, D uses 400 at £1 = £400.
It's not D's fault that they can't get approved for a mortgage, but they have to use and pay for more energy for reasons completely outside their control. As a result, they fail affordability checks for a mortgage and can't save a deposit anyhow with double the amount going on fuel bills.
It would be beneficial to introduce a system that helps people in areas of lower property values and perhaps that would lead to those areas being more likely to vote for the party who put it into action at the next election. But that's political, not environmental or ethical.
Effectively, the suggestion is a way to make people less able to pay the increased bills more because they don't have a way to live in the cheaper areas or mitigate their expenses through making home improvements or moving.