The four freedoms in the EU: Are they inseparable?

The four freedoms govern the movement of goods, persons, services and capital within the EU. They are the cornerstones of the Single Market and the common currency. Many citizens see them as the greatest achievement of the European unification project. Brexit has reignited the discussion surrounding the free movement of people - that is the opportunity to live and work in any EU country. Technically speaking, it is possible to separate the four freedoms, but does it make political sense?