The law of Supply and Demand is maybe the most rigorously validated theory offered by Economics.
It correctly predicts what will happen in each of your examples:
- Rent price ceiling, shortage e.g. Apartments in NYC
- Property tax increase, decrease in demand for those properties
- Utility price ceiling, shortage, e.g. water in CA
- Healthcare price ceiling, shortage. e.g. long wait times in countries like Canada
Whether or not any of those shortages/surpluses is good or bad is going to depend on your own personal situation. But you aren't even in a position to correctly evaluate that without something at least as predicatively powerful as the law of supply and demand.