No, not really. People who own their homes have a vested interest in prices rising, people who live in government-mandated affordable housing have no particular stake one way or the other, and people who rent at market rates often have low visibility into the fact that their rates are the result of a housing shortage and prefer to blame landlords for renting at prices the market will bear.
In the UK, since the early 1980's, it has been considered political suicide by a succession of both conservative and labour governments to not give money to the middle classes in the form of large increases in the value of their homes. This is one of the main reasons we have built about half as many houses as Canada since 1980, while having around twice the population.
Wouldn't this only work as a method of increasing middle class wealth if you owned 2+ properties? Otherwise, you have to live somewhere. You can't sell your house and unlock that wealth increase without spending it all on the next place to live.
People became obsessed with their home valuation. How much more money your house was worth since you bought it became one of the main methods of social boasting for decades, regardless of whether you were actually able to really profit from any of it.
Most of the middle class and up in the UK have a significant chunk of their wealth tied up in property (their own homes, then investment property), so not really.
People who value housing as a place to sleep rather than a financial investment.