The EU insists on free access to EU citizens to EFTA countries. Why? It is an ideological position.
You've been given plenty of benefits of the right for EU citizens to work in other EU countries - which you acknowledge - but then you ignore these reasons and repeat the word "ideological" like a mantra. It's no more ideological than insisting on the freedom of movement of microwaveable breaded chicken breasts.
The goal of the EEA is to provide a common market which is not a 1950s era "free trade" area - which only provided duty free import and export of bulk commodities like steel and coal. Part of being in a single market is allowing Italian bankers to work in London, British fashion designers to work in Paris, French engineers to work in Germany, Polish plumbers to work in Ireland, Irish software engineers to work in Amsterdam, etc.
I'm sure the UK would be happy with EFTA membership as long as they can apply restrictions on free movement of labour. By denying the UK the deal that they want they will hurt the EU as much as the UK.
This is delusional; it will not hurt the EU as much as the UK. Less than 10% of EU exports go to the UK while 60% of the UK's exports go to the EU. Sterling has lost 11% to the Euro since the referendum which indicates who the markets believe will be damaged by brexit. Worse for the UK is that they are a service oriented and exporting economy - exactly what is NOT covered by WTO rules - and trade deals on services can take a decade or more. The UK has already seen a massive contraction in inward investment - which has funded their trade deficit for years - and most economists and the BoE are predicting recession before the end of the year.
The UK is facing negotiations where they have no trump cards and will simply be offered the EEA deal or nothing - and they will take the EEA deal which is effectively non-negotiable and includes free movement of people plus a hefty annual bill. You should read the letter from the Norwegian minister for European affairs in the last Economist to get a picture for what the UK is facing.
There's about to be a 10 billion hole in the EU's annual budget if they lose the UK's contributions. Why not say to UK and Switzerland (who had contributed over 1 billion euros to enlargement projects in last 10 years) if you want freedom of movement restrictions, we want solidarity payments? Let the haggling begin.
They will not lose the UK's contributions - like Norway and the others they will continue to have to pay to have access to the single market. I'm willing to bet money that the net UK contribution will be within 20% of what they are paying now when they take the EEA deal. The EU can simply name their price and the UK will have no option - besides a return to pre-single market 70s stagnation - but accept.
The UK isn't perfect, what country is?
The UK was doing great; blessed by EU membership, as a service oriented exporter, to find itself in a position to be able to sell services to a continent instead of an island. London was transformed from a crumbling backwater in the 70s to a genuinely global city because it could serve an economic hinterland of 500 million people; able to compete with the great American cities, which have always had the advantage of a large hinterland, for the first time in a century. But all the benefits of being part of a huge market - last enjoyed when they controlled an empire - is threatened by the hubris of brexit. Just have a look at a historical graph of UK GDP and you will see a long post-war relative decline before joining the EEC.