What master account are you even talking about? That's not what this is.
The subject was a system being breached.
And the account you set up for a driver's license is generally different from the one for your health care. If you're reusing the same password for both it doesn't matter if they're linked by the same digital ID number or the same email address or just the same name and birthday.
In the UK's own post linked below (also in the OP), they describe what's more than a digital ID number. It's credentials. Which humans are bad at handling. And there are always implementation flaws, because we're humans.
The subject was a system being breached.
And the account you set up for a driver's license is generally different from the one for your health care. If you're reusing the same password for both it doesn't matter if they're linked by the same digital ID number or the same email address or just the same name and birthday.
A digital ID number isn't changing anything here.