"The EU seems to have an ideological attachment to free movement of people." I think you said. I am pointing out that the principle of freedom of movement for people is not based on ideology but on economics.
Do you believe that if the Americans suddenly decided that visas were required for citizens to move from state to state, that this would damage the economy of the USA? I believe it would. And so would it damage the economy of the EU to introduce 28 different points systems, conditions, delays, etc. to allow people to take up work in another EU country.
So why not extend it, why doesn't the USA have free movement with Mexico and Canada? And Brazil and Argentina? Or the EU for that matter?
The USA is a single fiscal-political entity, with social transfers to balance movements and a common language. People in California think about people in Wisconsin in a totally different way that people in Britain or France think about Greece or Poland. Accordingly, living standards within the US are such that you don't have a Britain-Poland type difference. A better analogy would be the US admitting Cuba as a new state. Do you think the US would within 2 years allow free movement?
But if it admitted Canada, it might well allow free movement in 2 years. That is the difference.
Free movement of people was not an issue for the UK when the EU had 15 countries of closer-matched living standards. It became a major issue only in the early 2000s with the accession of eastern European countries of significantly lower living standards than the EU core.
Your argument is in favour of free movement of people, full stop. It is not an argument - at least you have not made the argument so far - for free movement of people as an essential component of a single market of EFTA states, with restricted movement of people from non-EFTA countries into EFTA countries. Should the EFTA open up their borders to anyone who can find a job in an EFTA country within 3-6 months?
Canda and Australia, draw on a domestic labour market of 20-30 million, and use visa schemes to attract global talent. Their economic wellbeing puts forth a favourable comparison vis a vis the EU states including uk, france, spain, italy. So whatever benefits accrue to eu states from unfettered access to 400 m workers - they are not game changing.
So, why shouldn't Britain have single mimarket access without granting corresponding access to people?
If free movement of people has economic benefits to the destination country, then Britain will be the big losers, so why should the EU make it a red line in Brexit negotiations???
A purely economic rationale would see free movement extended to non-EFTA migrants. A purely economic rationale would continue free trade with Britain in the event of Brexit, because free trade without free movement is surely better economically for both parties than no free trade???
That is why I am saying the EU appears to have an ideological attachment to "free movement of people" within the EU member states.
The original question on this thread is not whether there are benefits to movement of people, or benefits to free trade but whether "there some economic argument which says that you can't have a free market without free movement of people?" I haven't heard a compelling one so far.