All EU citizens living here will have to register, without exception, even if they've been here for decades.
We can argue whether it's right or wrong, but we can't argue that's not the process, because it is.
As such, if they (or you, if you're an EU citizen reading this) want to stay, they'll be obliged to go through the registration process by June 2021.
Now, is it fair? Perhaps. It's certainly true that most other EU countries require registration. But the problem is that the Home Office isn't exactly famed for its accuracy, speed, or friendly demeanour. So there are bound to be many problems, edge cases and outright mistakes.
And since we're talking of a cohort in excess of 3 million potential applicants, even a very small problem rate in % terms will mean turmoil and upheaval in the lives of tens or hundreds of thousands of people.
Maybe, just maybe, because we'll be busy negotiating our new relationship with the EU (assuming Brexit Day has passed by then) the H.O. will take a different approach to its usual hobnailed boot stomping across peoples' lives, and be pragmatic and helpful about the problems, rather than confrontational.
I have no expectation that will be the case, but it's ok to hope they will.