Japan didn't have single family zoning, anyone could build dense housing anywhere residential in any of the major cities and they absolutely did, and yet it was never affordable. They have massively walkable cities, with great public transportation, and yet... not affordable unless you want to live in a 100 square foot closet that most north Americans couldn't even fit through the door on.
A bunch of US cities have no zoning and are still not affordable.
Zoning is a slight bottleneck, but it's not even close to the core problem.
I'm not saying don't change the zoning, go ahead, but expecting things to become affordable in a few years is an absolute pipe dream.
BC just did it, and developers are just shit talking the policy saying it doesn't change anything.