What about an EU citizen deciding to move to the US, Canada, Australia, Brazil or India? These countries were never in the EU. Did they therefore decide they don't need EU citizens? If not, why is the UK after it exits from the EU necessarily a less welcoming place for EU citizens than other non-EU countries?
To put it another way: if working in London, New York and San Francisco are going to be equally difficult to arrange, I'm not sure why anyone would prefer London. Housing is as expensive as NY or SF, yet wages are much lower. The weather isn't great either.
At any rate, "not sure why anyone would prefer London with the post-EU laws" is very different from "they decided they don't want me because they're not in the EU (even though there might be an otherwise nicely sounding arrangement available for me)."
Note that the freedom of movement in the EU means there isn't any "visa stuff" to deal with.
An EU citizen moving to the UK needs to fill in a form, to get a "National Insurance" number. The same would be required of a British citizen that didn't have one, for example if they'd been born and lived overseas before moving to the UK.
There are no other requirements that don't also apply to British / resident people moving within the UK.