In practical terms, also necessary to facilitate the functioning of the market. Most homes are sold by living people (rather than by their estates). They can't sell their house without someplace else lined up to move into.
Which is to say... I think there's less inventory than we would have seen had rates remained lower. But that's sort of unrelated to the issue of builders manipulating their rates of inventory creation (which I can't imagine they don't do, at least in response to macro-economic conditions.) The reason I think they should be treated differently is it takes a noticeable amount of time for a builder to build a house. First they have to negotiate financing and insurance, negotiate plans with the county, recruit a construction crew, etc. Home owners in the secondary market can respond to market conditions much faster.