I wonder if this could ironically end up worse for native cultures and the environment than OTL.
Absent Modernism, colonial Europeans continue having 8 kids each and continental Europeans have 5, rapidly populating the New World, Australia, and New Zealand up to the carrying capacity in the early 1900s. After that they begin to look at other places to dump off their surplus populations that are more difficult, like Southern Africa, North Africa, the Middle East, Siberia, and Central Asia, while others like Latin American's begin to look into the Amazon and Orinoco for space to try and avoid famine, or as Australia to tries to irrigate the Outback. This results in horrific wars of extermination against local populations and widespread environmental destruction.
Provided the European's win by the 21st century and run out of space again, during famine they perhaps begin to look at absurd places to dump their populations, like East Asia, India, the East African Highlands, or various Pacific Islands, and try irrigating virtually every desert in the world.