I am not so sure about the Common Travel Area exception. It did exist before the EU, certainly, but at the time the Republic did not have the free movement with France, etc etc: it had a hard border with Europe. As a member of the EU, that has changed. So now there is free movement into the Republic, there would be free movement via the CTA between the Republic and the North, and free movement between Northern Ireland and the rest of the UK.

This may happen, because Parliament doesn't seem to think at all about Ireland unless it is forced into it, but I think there is only one way of avoiding it while still having a CTA: much more frequent ID checks of all UK citizens as they go about their daily business to find people who have got in by some means. I think it very unlikely to go anything like this far, but in extremis it would be police demanding to see your papers whenever they wished. We have already gone a fair way down this road as it is, with identity needing to be proved when getting a job, or renting a flat, for example.