This really depends on the details of the market. Much of the housing stock in NYC are Co-ops that require the owner to use the apartment as their primary residence. (My building is 100% owner-occupied, though we do allow subletting for a couple years.) You can compare prices in these buildings to restrictionless condos and see how much effect investors have. It is noticeable, but not earth-shattering. Many people that live in co-ops probably could have bought a condo if it's what they wanted.

Yeah thats just not true. You are competing against both but not on every home.