Where the whole icon thing sort of works, is with tools where the words won’t be able to communicate what a tool means anyways and. when there are too much for (e.g. the tools in photoshop)
It's also a neat way to resolve issue with text-only buttons in multilingual software. From time to time, I find myself in front of an OS, an app or a website that's familiar to me, but is set to a language I don't know. Having an icon next to the text is very helpful then. That said, it's a rare case, so if I had to choose just one, I'd prefer text over icons.
Imagine that users of an NHS website are infrequent at best with a large number of new users.
[1] https://annhjelle.wordpress.com/assignments-2/assign-12-spac...