Are EU citizens in the UK the only officially undocumented legal migrants in the world now?

https://www.theguardian.com/politics/2020/sep/26/eu-citizens-uk-brexit-settled-status-jobs-banking-healthcare

The entire thing, the application, the status and the many empty promises made and reneged on, it means zilch.

We’re still vermin.

So far, at least one person was blocked from boarding a flight for the same reason as why the people in the above article in The Guardian ran into hurdles. The status means zilch. You have no legal proof of it. 

But what else can people do other than either go through the farcical rigmarole or leave?