Per Capita isn't the right approach, but per household is also the wrong approach. Household size is effected by, well, the number of housing units. A state that has historically suppressed the number of housing units will have higher housing production per household than a state with equivalent population and housing production that historically hasn't suppressed housing units.

Adult population is a better approach

Personally, I'd measure change in housing stock relative relative to change in adult population (completions - demotions) / change in population 18+