Tax numbers have no bearing at all on your right to work. If you work legally in the UK for a while then you get a national insurance number but if you then leave and your work visa expires, your national insurance number remains as an identifier.

Can't say until the implementation is revealed, but the person you replied to pointed out that fraud at the application stage is a problem.

Checking for right to work has been legally required for over a decade. Checks in the formal economy are now routine. Can sometimes be a nuisance, like for my friend who doesn't have a passport and his driving license was issued before those went photographic.

I have never seen a report of a business ending because of a fine. I have seen reports of hospitality business having to close because they lost their alcohol licence, where the licencee employing illegal immigrants was deemed not to be a fit and proper person.

Recently the prime minister delivered a speech and then later walked the entire thing back saying that he hadn't read it before delivering it. A man who has declared that he is nothing more than a text to speech engine probably doesn't have a plan.