Thanks Robin - that's a very good question, and your understanding is right as far as I know. In theory at least, CfDs should save bill payers a lot of money when electricity wholesale prices are high.
The thing I find tricky, though, is seeing where the money from this CfD effect had actually gone. You'd expect to see really big savings from CfDs over the last year, and I think these are baked in to Ofgem's price cap calculations, but it is surprisingly hard in my experience to work out where the payments have gone. I've also seen stories that some renewables operators haven't actually taken up their CfDs, but I'm not clear how true or important that is.
Ultimately, I think the CfD approach is very helpful - it gives confidence to both generators and energy consumers about what energy prices will be - but the change in economic conditions mean the recent CfDs have been set too low. It might be a matter of just tweaking the CfDs, or it might be a question of rethinking how we fund energy projects altogether.