Unfortunately the housing market is rather more complicated than simple supply and demand. Houses aren't lemons or bicycles.
Where you sit on the 'available income for housing' curve determines the location and quality of the house/apartment/tent you live in. If lots of people with higher incomes appear, then you get moved down accordingly. If lots of tourists with higher propensity to spend on temporary accommodation appear, you get moved down accordingly. If lots of 'funny money' turns up looking for a place to be parked, you get moved down accordingly.
Where people get distressed if is the location and quality that they can afford is not reasonable to them (either actually or by their perception).
Building high quality well-located homes may help (if that is even possible), as everyone can 'move up' to the next rung on the quality/location ladder. However you may get induced demand, as the slight drop in prices brings more high earners/tourists/funny-money, in which case normal earners will not see the benefit.
Alternatively, restricting high-earners/tourists/funny-money will move normal earners up the ladder, without having to lay a single brick. However there may be some economic downsides to that, depending on what exactly is proposed.
For example banning AirBnB would likely be a large net positive to most European cities.