No, but.
In reality EU citizens never had a freedom to come and go as they please. They have never been subject to immigration control, but always have been subject to residence restrictions.
For example, there is a concept of "exercising treaty rights", which is: employed, self-employed, student, self-sufficient (with medical insurance). De jure, an EU (non-Irish) citizen who was not "exercising treaty rights" was residing in the UK illegally. There are even powers of deportation granted to the government under EU freedom of movement - not currently used against French grannies, of course, but against Roma rough sleepers.
I am a Remainer, but I find these complaints about the new registration scheme disingenuous. It is effectively a mass amnesty, as a significant number or people were in breach of the "treaty rights" condition. I personally find it incredible that someone could move to another country, cross the border, and not bother to check the residence requirements even once. If my Polish hairdresser, with very limited English, knew about the requirement to have private medical cover if she is not working, how come all these highly educated expats campaigning for EU citizens did not?
It is probably a sense of entitlement or superiority, I cannot explain it otherwise. My immigration solicitor says she cringes inside every time when a white, middle-class and native-English-speaking potential client (Australia, Canada, US, NZ etc) contacts her for advice with "there must be a minor misunderstanding here". Because, in her experience, there is very likely to be a long history of overstays, breach of immigration laws etc., all explained by "I did not know this", which she translates in her head as "I thought white people are above this stupid immigration law".