Yes, indeed they do. But our tax collectors don't have the time and resources to challenge the convoluted tax returns of the wealthy. So they make the lives of Joe and Jane the small business owner a living hell. A totally new system, plus a Tobin tax on all financial transactions, is needed.
Plus, housing is not expensive because the rich don't pay their fair share of taxes (beyond the interest on home loan deductions on several homes). Once houses became the commodity of choice in credit markets and we stole normal people's houses to bail out the banks, the bubble was was quickly re-blown. Repackaged mortgages are still the primary currency of investment banking, so they are kept in the way overpriced. Note: https://medium.com/@daneke/the-landlords-game-the-grand-dispossession-of-america-49513bf9eb4