For me, this is akin to the trade discussion. We have always been able to trade internationally, that isn't really what trade deals are about. Rather, by virtue of unifying regulations or reducing/removing tariffs, they're about making trade easier between nations. It's the same with people. Free movement made it as easy as could possibly be to both travel within Europe and settle within Europe. It's quite possible that people will still be able to do things, but the chances have to be pretty high that red tape and paperwork will increase, and thus make it both harder and more expensive to do so.
I mean even a relatively simple example. If EU nationals have lived in the UK for 5 years and wish to gain settled statement, the indications are from March they can apply for that. It's 'relatively' straightforward (although I won't hold my breath on that, and frankly think it's a disgrace that they are losing the right to vote in local elections), but even with it being relatively straightforward, it's still costing £65. Now you might rub your hands together and think wahay, a windfall, but the NHS has agreed to pay that fee for EU staff, because they appreciate the value they bring, so multiply that up over the 63,000 EU nationals working in the NHS and you've spent £4 million on stuff you hadn't previously needed to spend.
As has already been shown in numerous statistics, there is already an impact on numbers coming and working here, which given that the evidence shows they are net contributors to the treasury, that in itself is sucking money out of government too.