There is a lot of misinformation about green levies.
It was once claimed that they were 25% of our bills; that was never the case. They account for about 7.5p per day or roughly £28 per year - a couple of coffees and a blueberry muffin per year. Good grief!
The CfD works both ways, as Suff says. If the strike price is low the Govt makes up the difference, if the price is high the treasury coins it in. The customers notice no difference.
The Ofgem price cap is just that - a limit. Suppliers, not producers, will price to the hilt. They could charge lower... but the cartel won't let them.
Our energy prices (given inflation) are not that much more than they were pre the energy crisis, even with those damned green levies.