Housing hasn’t been the biggest problem in Japan since 2000s. Like it is, but not the biggest one. Yet the birth rates have never increased after the initial bump.
People, especially women, have other things they can spend time on instead of giving birth to 3+ kids.
Japan is an ethnostate with unique problems and situations that no other country shares.
I agree with you that other factors, such as cheap international travel and constant bombardment of people's highlights on social media, make it less attractive to invest in having a family.
Still, housing is a huge problem for Western Mediterranean Europe (Spain, Portugal, and Italy) and most of Latin America (Mexico, Brazil, Colombia).
People, especially women, have other things they can spend time on instead of giving birth to 3+ kids.