This should be illegal. There's no good reason why you shouldn't be able to split up your 13,000 sq ft lot into smaller lots and sell those separately if you want to. Setting some reasonable state right-to-split-lots bill might go a long way to helping solve the housing crisis.

A little late response to this, but many of the minimum lot size laws are rooted in historical racism and classism to prevent people of the wrong type from being able to move in to the neighborhood. In many areas there is a lot of foot dragging to change any of it. Typically the language used to oppose it is "traffic" or "neighborhood feel."