I hate to be pessimistic and there are elements of the idea I like, but when reflecting on the issues at hand this feels like popping the toaster because you smell burnt toast, but the rest of the house is on fire
This ID system is touted as somehow stopping illegal boat crossings (the current political hot topic in the UK) because it will apparently somehow stop illegal work. This is obvious nonsense. Employers are already supposed to do ID checks and face heavy fines for employing illegal workers. Illegal employers obviously don't bother with such checks and pay cash in hand. They will continue not to bother doing any such checks, with or without ID cards.
A great deal of illegal work is actually caused by arm's-length employers such as food delivery apps and other similar platforms. These companies already do fairly robust ID checks. What happens though is people rent out their accounts (often for surprisingly small amounts of money) with the ID check already passed to illegals who actually do the work. The problem is nothing to do with ID checks, it's the fact that the employer never sees the employee in person and doesn't verify on a day-to-day basis who is actually completing the work.