Yes! Buying your own home is the ultimate form of rent control, even though property taxes increase over time (and its even worse in CA with prop 13). Very unfair.
If we wanted to make the market fair, we would disallow home owners all together. This effectively happens for most people in some places in Europe. Also, I heard of some places in Europe where if you own your own home, you have to pay some extra tax vs. what you would have paid in rent. I think Switzerland? They also had some form of rent price control, although this just made it really hard to rent an apartment even if you were willing to pay more. These are fairly complex systems that all give advantages to existing residents (so moving to Europe for two years to do a post doc is much harder than it would be if you did that in the USA).
If we wanted to make the market fair, we would disallow home owners all together. This effectively happens for most people in some places in Europe. Also, I heard of some places in Europe where if you own your own home, you have to pay some extra tax vs. what you would have paid in rent. I think Switzerland? They also had some form of rent price control, although this just made it really hard to rent an apartment even if you were willing to pay more. These are fairly complex systems that all give advantages to existing residents (so moving to Europe for two years to do a post doc is much harder than it would be if you did that in the USA).