More grass -> more rabbits -> less grass -> less rabbits -> (loop). You can mix different rabbits in, but the cycle is fundamental.

Humans aren't rabbits. Humans tend to have children in inverse proportion to the amount of grass, poorer people having more children than richer ones. Of course it's not a direct correlation, or a simple one, but the effect is there.

Agreed. What does this tell us in the context of this discussion?

Returning to the initial point, should people just build more houses?

More houses in locations people want to live in, yes. In the end, even leaving house prices aside, a larger population needs more housing, and the UK has been underbuilding several tens of thousands of units a year for decades.

I think you just proved my point.