Just to be a bit nitpicky here...
Allowing a customs union without the four freedoms (such as freedom of movement) is not unusual or exceptional. Turkey has a customs union with the EU without these freedoms. The four freedoms are seen as integral to the single market, which is very different from the customs union.
What is a partial concession from the EU, in the interests of avoiding a hard border, is to allow NI to benefit from some aspects of the single market without the four freedoms. Ironically, it is the DUP who hate this element as it makes a distinction between NI and the rest of the UK, even though being in the
backstop would actually give NI a pretty good competitive advantage.
You are right that the EU’s first preference was for NI alone to remain in the customs union (and elements of the single market), rather than a UK-wide customs union, but it’s not related to the four freedoms. Long but thorough explanation of the negotiations:
https://www.rte.ie/news/analysis-and-comment/2018/1207/1015924-brexit-backstop-uk/