Consider Toronto as a counter example. That city tore down parks to build condos. That didn't rein in prices. Now, the affluent foreigners have 3-4 condos to go along with that Maserati.
DC has torn down a lot of things to build housing, and has converted former industrial properties into new neighborhoods (NoMA is an example). DC itself can't get rid of many of its parks because the National Park Service controls many of them, but neighboring jurisdictions certainly have gotten rid of parks in exchange for high rises (Arlington, for instance).
What matters isn't what was replaced, but how many net new units are built vs. demand for new units. DC is falling behind. I'd imagine that Toronto has similarly fallen behind.