I agree. I just don't see what problem they are going to resolve.
If you want to legally employ someone, you need to be sure they are allowed to work here e.g. by them proving they are a UK citizen or having a visa etc. A digital ID will just be a further way of doing it, but you could just as easily insist everyone has a passport, which at least has other benefits for the individual.
If you're working illegally, no one cares and they're not going to check a digital ID.
They've already said you won't need it for NHS treatment and you apparently won't need to provide it for anything else or carry it, so it's either a pointless waste of money, or the door to something else they're not stating.
Add into that, it'll be a government IT system, so several years late and massively over budget, and will probably have out of date security meaning it'll be hacked by China/Russia etc within about a week of it going live.
Other than that, I'm in favour...