In the case of expensive urban areas it kind of does. High housing costs mean that literally everything in an area is more expensive. All services and all good

In the case of expensive urban areas it kind of does. High housing costs mean that literally everything in an area is more expensive. All services and all goods require human labor - people to load and unload trucks, stock shelves, stand behind registers, prepare goods and services etc.. High rents are a massive transfer of wealth over time from everyone else to landlords. So yes, increased housing costs do make all local services cost more, at the expense of the general public and for the benefit of landlords.