In some ways it was worse than that. Rome practically founded the concept of a lightly restrictive immigration policy.

A big stepping stone started with Julius Caesar who wanted to gain further control over the senate by adding Gaul representatives (which is a big part of why he got stabbed to death during the Ides of March).

And I think the idea evolved under Augustus Caesar with the idea of Romanizing the barbarian territories and incorporating them into the empire. This of course backfired, multiple times. Not that the idea was totally unfounded, especially since such measures had seemed to work out when they employed it in more civilized territories like Greece and Asia Minor, but ultimately it was repeated and led to failure, time and time again.

It finally ended when barbarians totally took over Rome itself. A final and well earned disgrace when you had barbarian warlords ruling over the Romans within former Roman government homes and chambers.

There's a certain irony with how leftists have been trying to label the Roman empire as fascist for the last decade or so, in spite of how some of their policies so closely mirror the modern left.

(I may be off on a few details, but I think this is a generally accurate summary. Feel free to correct me if I'm incorrect on anything.)