It's inversely correlated though. It's been known for decades now that as countries become more wealthy and well off, the birth rate falls. If what you stated were actually true, Africa would not be the continent with the fastest growing population because it's a complete shit hole with barely functional countries at best. Yet despite being hell on earth, they pop out more kids than anyone else.
The lower birthrates in western societies are largely an effect of increased urbanization and overcrowding. John Calhoun's mouse utopia experiments found that overcrowding led to population decline and what he called behavioral sink, which has striking parallels to the kind of degeneracy that's seen coming out of large cities today. Cities only have growing populations because people keep moving in to them. They're not stable on their own.
South Korea has a population density of almost 1,400 people per square mile for the entire country which is already higher than any US state. About half of the population lives in the Seoul Metro area where the population density is over 5,000 people per square mile. Of that, about 40% (about 20% of the country's total population) live within the city proper which has a population density of 41,000 people per square mile.
Is it surprising that no one wants to have kids when they live in an environment that crowded?