If they just subsidised the standing charge and kept the unit rate the same as the market rate I would be happier but it seems from the maths the subsidy is more tilted towards higher usage houses
But unless you use pretty much no energy at all, the standing charge is a small percentage of the annual bill. At the current price cap, it's a little over 10%.
If they did what you're suggesting, then it would knock a couple of hundred pounds at most off a £5k pa+ bill that would still destroy the finances of average income households in 2-3 bed properties using a typical amount of energy.
On the matter of profit, this is due to increased global demand for a finite and reducing supply of energy. The companies who we as householders buy our energy from are not making much, if any profit at all, it's under £50 a year. They could sell us energy at cost, and it would barely change the size of our bills.
They do need a windfall tax on the global mega corps who extract and produce the energy, but that's a separate issue.