[notahacker]

Arguably unifying of back-ends are more important than the visual design for consistency and ease of use though.

The introduction to the article shows several different styles of registration or login button used across different US govt departments, but the key point here is that they're all separate user identities requiring separate logins. Making visually identical login flows that actually require different credentials to log into separate services actually makes things worse for periodic users of multiple government sites. What's needed as an even higher priority than changing the buttons is a uniform OpenGovernmentID everywhere it makes sense to do so

Priority number two for ease of use in government websites would probably be fixing link rot, since government websites have a horrible tendency to deep link to other departments just before that department's site gets reorganised or renames (and departments whose sites were replaced by the gov.uk platform unfortunately are no exception)