Re: Amsterdam
The UK isn't that special and amazing that it will get exemption rules for all 66 million people.
Let's wait and see...
And while doing so, consider the status of people from places like the Isle of Man and the Channel Islands. Neither is in the EU, and people with British Islands passports do not benefit from the EU rules on free movement. All the same, most EU countries accept such travellers as they do any other European traveller, at least for brief visits. I'd imagine there would be more paperwork if someone from those places wanted to settle or work permanently in the EU.