They still have the ability to outbid if they want to.

Are you familiar with price elasticity of demand? If they have to pay a larger share of their wealth, they will buy fewer. If houses cost $100, couldn’t you think of reasons to buy more than one, where you wouldn’t if houses were priced within what you could afford but much more expensive than that?

income equality

IMO the distinction between income and wealth inequality is very important here. Income inequality is about jobs, wealth is about accumulated capital.