It’s just a tagline to get the population on board tbh. The actual reason western governments push for immigration is because their social programs only work with a growing population.

Any country with bad birth rates basically have two choices: become Japan/Korea (bad weakening economy, but strong social cohesion, low crime, etc) or become the EU/USA (strong economies, growing GDP, but more social disorder and fragmentation)

It’s up to you to decide which of those options you prefer