Wealth distribution is important, because very rich people disproportionately buy up limited-supply assets in order to earn passive income on them. In densely populated places, that includes assets like homes, which pushes up housing costs.
Housing costs often aren't included in popular measures of inflation. If you do use an inflation measure that includes housing and all other everyday expenditure, then I think it's a reasonable to argue the baseline going up is good enough.
Unless someone buys up so many properties they can start unilaterally increasing prices, the problem with housing going up isn't rich people buying them and renting them at a market rate. It's the amount of demand vs supply that does it.
And you're right - this is possibly the single biggest issue that's a downgrade for people vs their parents/grandparents, and it's a huge one. But the problem needs to be attributed correctly.
More very rich people looking for somewhere to park their money and earn returns means more competition when you want to buy a home.
I agree it doesn't necessarily mean rents rises. You might actually expect higher price to earnings ratio with more wealthy people competing to buy assets (see also stocks).
But it will lead to the shrinking of the home-owning middle class.
That's not to say there isn't also a problem with lack of supply.
Housing costs often aren't included in popular measures of inflation. If you do use an inflation measure that includes housing and all other everyday expenditure, then I think it's a reasonable to argue the baseline going up is good enough.