BOSTON—Boston has bristled with construction cranes for years. But the region is still straining to keep pace with growing housing demand, and the city needs more help from reluctant suburbs.

The city expects its population to reach almost 760,000 by 2030—a 23% climb compared with 2010. To accommodate growth, the Metropolitan Area Planning Council estimates the 164-municipality metro Boston region will need to have added 329,000 units of housing between 2010 and 2030. But the area—which ranges from old industrial cities like...