Blackmoor Vituperative

Is this sentence grammatically correct?

The vast majority of people never leave the planet of their birth.

“Majority” is the subject. It is implicitly plural. So it seems to me that “cities of their birth” would ordinarily be correct. But this seems to imply that each of the people is born in more than one city, which is nonsense. I think that the above sentence is correct, but I am not certain. Hmm.

I have tremendous respect for people who learn English as a second (or third or fourth) language, and who become as proficient with it as native speakers are.