It's a much bigger group than homeowners. Banks don't want housing prices to fall, since then homeowners start foreclosing and then banks lose interest payments and own undesired property. Cities don't want housing prices to fall, since they were counting on money from developers and property taxes.
Property taxes are relatively independent from the absolute value of the property. Only the relative value of a property to other properties in municipality determines property taxes.
I don’t agree with this take, we’re overly simplifying the nature of housing here. It depends on the housing mix as well. If the vast majority of the pro-housing prices crowd is heavily invested in single family residential then they should favour widespread upzoning and deregulation of apartments because that would increase the value of their SFHs through two mechanisms: 1) presumably single family homes will be destroyed so any remaining single family homes become more valuable and 2) every single family home is now a potential townhouse or high density building which increases the value a developer would pay for it.
Are there any serious objections to that line of reasoning?