The point is, the apartment owner pays property tax and collect rent from tenants to pay for that. If property taxes go up, property owners raise rents to compensate. So the tenants are paying the property tax, albeit indirectly.
Its actually much more complicated then that, depending on factors such as the propensity of landlords to cease renting out units if their profit decreases, the propensity of renters to shift to smaller dwellings in the face of rent increases, etc.
Also, 1-year leases are typical in the U.S. (at least Philly/NYC northeast U.S.), so from that contractual perspective, your rent can go up every year and that's totally legal.
Your mistake is assuming that people who bought up housing stock are guaranteed future profit on their speculative investment.
Step 2) Force out investor class and/or repossess properties out of tax adjudication.
Step 3) Public housing!
How does this logic work? Building apartments becomes a bad investment. Then developers don't build apartments. And somehow constrained supply is supposed to result in lower prices?
You can say the market won't let it happen, but the second case is the current real estate market for the town I went to school in.