The public ownership rental option goes nowhere without a capability to acquire (and retain) properties for the programme, and the ability to move unproductive or underproductive real estate into same.
California's property tax situation (e.g., 1977's Proposition 13) makes this an all but unsolvable problem for that state. Short a countervailing proposition, a (state) constitutional amendment, or a state or federal supreme court reversal, that law is going nowhere, and is pretty much a Land Value Tax's antiparticle / kryptonite.
One potentially promising alternative is the growth of land banks, mostly in the Eastern and Midwestern US, notably Illinoios, Ohio, and New York, possibly elsewhere. Though not based off a land value tax, tax-delinquent properties are acquired by the land bank which then attempts to return them to productive use. Pairing the land bank and public ownership rental models strikes me as a potential viable route to expanding both concepts.