The supply of housing is an important problem (for cost of living, equitable conditions for the poor, etc), but it's not clear how directly related it is to homelessness.
That is, if you lowered rents 50% through increased housing supply, it's not clear how many formerly homeless people will now be housed.
one of the many reasons local governments don't approve housing is that tax revenues from housing rapidly decay to 0 while services for the additional residents cost significantly more than 0
do you have any references for this? how does the tax revenue 'decay' to 0. Prop 13 doesn't reduce the tax over time but fixes it at a certain amount upon purchase (if the property is new) or transfer if it's sold.
All new houses and transferred properties are taxed at the value they were purchased.
No, I have no citations for the claim that inflation is sometimes above 2% or for the claim that the inflation rate for government services (which includes the cost of buying local housing for government employees) is sometimes above 2%. If either of these were true, the tax collected on a given property would increase in nominal terms but decay toward 0 in real terms.
Unrelatedly, Brisbane found that they could raise 9 times as much revenue and provide 0 times as much additional services to residents by approving hotels instead of housing. https://brianlui.dog/2018/08/01/housing-shortages/#_edn4
That is, if you lowered rents 50% through increased housing supply, it's not clear how many formerly homeless people will now be housed.