> Most businesses rent so property holders would feel the tax burden and rents would go up significantly.

Property holders would feel the tax burden, decreasing the net revenue from rent, and decreasing property values.

Rents are already at "market rates", and property values adjust to reflect the return on renting property. There might be some short-term price fluctuations as property owners try to maintain their existing margins, but an efficient market for real estate will stabilize rents close to the existing prices. The real losers would be those who purchased real estate assets expecting a consistent future return.