You know it's possible to regulate prices with laws, do you? The thing you said is not a law of nature, just something we agreed on. And we can change our mind.
You can't legislate what people value, but you can change things so they value them more or less. I think the most promising thing would be to convince companies to create jobs in places where the cost of housing is lower.
You know they did just that in Venezuela, with noble intentions, do you?
There has to be some selection. With free market, the selection is about how much you can or are willing to pay. Cap the rents and other criteria will be used. In many cases, more or less legal froms of bribery will make up for the gap in value.
Another common thing that happens when rents are capped is that landlords are going to make sure that they are only renting to the rich, because the rich are less likely to default. How are they going to know that you are rich? Obvious ones are to look at your bank account (privacy?), but unfair criteria like race can also be used.
You can also become communist, have the state take all housing and redistribute them "fairly". I think it is an area where communism actually works, but it probably won't be well received in the US...
Price controls do not work and are actually damaging because instead of trying to balance supply and demand they make the imbalance even worse. They do not remove the pressure of supply and demand, which continues to be at play.
I'm not trying to be coy, I simply haven't seen a viable alternative with details. And since most of the world converged on using money to decide allocation of resources, I'm wondering if the alternatives have significant drawbacks.
I understand that wealth begetting wealth, especially for generations seems unfair. But the solution to that doesn't have to be lottery or waiting list of housing. If the goal is to spread the wealth around more evenly, then that can be accomplished with higher taxes.