Very grateful to John Naughton for pointing to this article, which explains the problems and some of the solutions and which seems like an obvious dose of sanity.
Ultimately, like many discussions around solutions to climate changes, this is a “yes, and” rather than an “or” choice. We can, and should, build more transmission capacity and storage, whilst reforming the market such that the UK’s phenomenal success in deploying wind power can be finessed to more precisely match our energy needs.
I'm sure I don't understand all the details, but I feel as if I understand more than I ever did before.