I think this is an important insight, even though it is a bit unfair to put the blame on the woman like that. The problem is rather the concept of the nuclear family and the expectations it puts both on the women and the man and all the assumed to be necessary lifestyle that comes with it. Saint Andrewism made a video about more or less this recently.

So yes, due to sharing expenses and some tax incentives for nuclear families it does in theory appear to be cheaper to live together like that, but in reality people have plenty of other forms of living, often cheaper and more fulfilling (or not).

However women do seem to be still more invested in the model of the nuclear family as it is sold to them as the model that gives them the most autonomy as a stay at home mom. This is a myth, but one hard to break, and for someone quite opposed to the concept this makes it very hard to engage in romantic relationships.