During housing shortages in New York, construction companies used their resources for office buildings, industrial plants, and other commercial buildings instead of much-needed apartments. Rent controls did not apply to this type of construction.
Where medical care is subject to price control, people in lesser need monopolise the practitioner’s time because they incur little to no cost for demanding it. The NHS in the UK gave 12-year-old breast implants while 10,000 people waited 15 years or more for surgery.
A ceiling on how high prices can reach makes a product available to those who do not most need it. It also diverts resources away from being used in price-controlled products. In the real world, where resources are scarce and efficient allocation should be the goal, they incentivise inefficient use.