The problem with “just raise taxes solution” is that there is no guarantee that money from taxes is going to be evenly and correctly distributed and spent.
This might work for relatively small and single-nationality countries.
What if you raised property taxes with the expectation that the tax isn’t often actually paid? For example, if every piece of real estate had to be traced back to the natural person owner(s) and the property is taxed at the individual level but graduated. Significantly. So no tax at all on the least valuable property you own, 50% tax on the next least valuable property, 100% tax on the next least, etc. With the goal being to significantly disincentivize the hoarding of housing (which is both a necessity and a form of “wealth” building) rather than to collect and redistribute wealth? Even though the ultimate outcome would (hopefully) be redistributed wealth.
Yes, a progressive tax over all your possession is a much better solution than just raising prices. People with high income don't really care about high prices and have enough opportunity to delegate these costs to others.
The taxes wouldn’t be intended to raise money but to distort markets. Instead of worrying how the extra money could be spent a raised tax could offset a compatible tax break. I.e. raise taxes on landlords, lower taxes on owner occupied housing.
This might work for relatively small and single-nationality countries.