What evidence exactly are you looking for? If you compare two different cities with different housing densities, you're not only changing the housing density but (likely) also the value of the housing (since it increases availability of services and so on). It's not possible to magically adjust one variable while not touching the others.

However, if the prices in silicon valley were, say, 30% lower than they are now due to zoning which allowed more housing, would that constitute as evidence? You could still say that the "prices are high, higher density housing doesn't work!" - even if the higher density housing would've decreased prices by non-trivial amounts.

In any case, it's weird to see people objecting to basic supply and demand when it comes to housing.