That's not a solution, that's another problem. Japan, Europe, most of the USA, and even parts of Africa already have birth rates so low that they're below the replacement level. This causes workforce shortages, requires mass immigration, and causes several new problems in both host and guest countries. Japan itself is in a nose dive. Adult diapers outsell infant diapers. Less people = less customers = less money = less jobs.

"what land? There isn't a vast reserve of untapped productive land lying around."

That's what I thought. But there is. It's in Africa. A large swath of land the size of France got grabbed up during the 2007 Great African Land Grab which no one seemed to notice or care about other than the Oakland Institute. Communal lands were bribed and bought up for as little as 18 cents a hectare with the promise of infrastructure improvements and jobs. Few of which came into fruition.

No, it doesn't require that: without universal free contraception, economic development and, particularly, strong social safety nets reduced birthrates in much of the developed world to below replacement levels. Note that this is less true of the USA than much of the modern developed world because while the USA has good aggregate economic output, it has fairly weak and unreliable social support systems for a developed country.

People have more children when children are your insurance against poverty due to age, disability, etc. -- as they have been for most of human history. When that becomes less true, they have fewer children.