The theory says that new units are added when prices are high and building new units is practical. Building new units is inhibited, therefore prices go up, exactly according to the theory.

The problem isn't the theory, it's the inhibiting of adding more units.

There's been an assertion of a "body of literature" but no pointers to it, no assessment of the data quality, no assessment of the validity of the interpretations, etc.

There are entire bodies of literature based on zero evidence, due to epistemic doubt about evidence as grounds. For example, critical geography actively rejects basing their body of literature on evidence, and reaches conclusions about gentrification and displacement and housing production that are quite contrary to both the evidence and standard economic theory. Yet the work of critical geographers is endemic in public policy around urban planning and political debates on housing production in urban areas.

I would agree in general that theory must change to match the evidence, but again, what evidence is at play in any of this thread?