Companies know the usage of their customers.
Government knows the house types.
It would be interesting to look at outliers and wonder why their use is high - so if you have a 3 bedroom house, why is your usage that of a 5 bedroom?
Is there a good reason or are you wasteful?
It is complicated - but should people who waste energy be subsidised?
Interesting, perhaps. But we are talking about practical and cost-efficient solutions here, not an academic study on anomalies.
Have you seen the UK track record for Governments implementing IT systems, how long this takes, how the costs spiral? How many get scrapped after billions spent on them without ever being implemented? And that is with years to implement whereas this needs resolving in six months.
It's delusional to think they could implement such a complex system in six months. Just "performing the review" will likely take them most of that, to come up with a "strategy".
And implementing support only through existing assessment systems such as pensions/ benefits will leave many people in need to fall through the gaps and be very far from fair because it ignore all of the complex factors impacting usage that I, and you, and many others have described. It will also mean the support scheme loses public support because many people who really need the support will end up paying for it but not receiving it: not viable.
So while imperfect, there does not appear to be any viable solution that can be implemented in six months to do anything other than make any relief offered universal. This could of course (as it has been) be topped up with additional relief for certain groups who are easily identifiable from existing systems as having a need that would lead to higher usage. But the idea that some complex algorithm that will factor in all relevant circumstances and spit out a "fair" Government contribution per household is either theoretically or practically possible to implement in six months - when they have not yet even discussed on what basis they would do so! - is farcical.