When Pinnacle Housing Group offered below-market rate apartments at its Brickell View Terrace development, it got 4,000 applications for just 100 units at the high-rise planned for one of Miami-Dade’s most expensive corridors.

Priced at about 90 cents per square foot—less than half the average going rate in Brickell’s prestigious financial district—the units created a furor among low- to moderate-income renters looking for a spot near downtown Miami.