A further point, The logistics of introducing control on EU migrants are horrendous. May wouldn’t have survived six years as Home Secretary if she didn’t realise that. We have no way of distinguishing (or enabling employers to distinguish) EU nationals settled here from date D from those arriving after it. We have no intention (I hope) of requiring visas – so no way of stopping EU nationals coming as tourists and then working. And there’s the open, and uncloseable, border with Ireland (and quite possibly Scotland if hard Brexit were to be tried).
The trick of states(wo)manship is to take constraints like that and sell them as virtues.