The problem is that the old single family housing unit is occupying valuable land which could better serve multiple families at a higher density.
City cores are about increasing the density of human population so that network effects increase productivity, decrease cost, or both thus raising the efficiency of limited resources.
The correct way of regulating the cost of a city is based on a combination of the usable area occupied (probably a 2-dimensional area unless someone is able to build above/beneath a given property), the number of tenants there and the 'useful floor space' (exclude hallways, balconies, etc) they receive for whatever their rent is (property taxes are rent paid to the municipality for use if it's commons resources; IE being close to other things and being able to reach them).
The government should be driving /down/ the price of housing when it is too high by pushing for the construction of denser housing in the urban core to drive the market curves from the supply side.
The government should also have it's tax structure setup in a progressive way (penalize rents not in the lower half of the equilibrium, including home owners that outright own their home (and thus only pay property taxes)).
When the market is over-saturated (as it would be if an area is deflating), it should be supporting the existing prices on the market by keeping taxes high, buying back properties that are sub-standard, and focusing on their re-development in to civic goods; some examples of which are parks, arts facilities, or facilitating new small business experiments.