If there are 10 million people looking for a house with a budget of $1000/month for rent, and there are 20 million empty houses but they're all set with a rent of $1500/month, then the landlords can choose to lower their rent to have some income....Or they can just let their houses stand empty, advise people to co-house, etc.
There's a glut of high-priced housing units and a shortage of smaller and especially cheaper housing units at the moment. New builds, though, have to comply with ecological restrictions, zoning restrictions, etc etc (some of which are not as strict in the USA as elsewhere, but still) and this drives up prices. In Belgium, finding a spot where it's legal to build a new house is becoming a problem - we're too built up and we want to restrict further loss of open space to buildings. Therefore, whenever someone does have a plot of land zoned for housing, they're more likely to put up a block of 6 or 8 apartments than a single family house. Much higher return. Either way, newly built housing has to be nearly energy neutral (BEN is the literal term used meaning exactly that - "almost energy neutral"), either by producing a large part of their own energy (solar panels, wind turbine, water wheel,...) or by being isolated enough not to lose much. Practically, they need both. This drives up construction prices, along with the current shortage of some materials and, of course, increasing labor costs. Building a "cheap" or "affordable" house simply isn't worthwhile, profit-wise.
In the US, house prices have skyrocketed, for a number of reasons, one of which is greatly reduced first home ownership with a large part of the market falling into the hands of corporate real estate agencies which are interested only in high profits and have pushed their prices on everything up as high as they can go. There's been a visible (in charts) move of people to houses one or two categories "down" from where they could've gone a decade earlier, thus leaving more high-end properties empty and low-end properties with high demand and the lowest incomes to fall out of the housing market all together.