Because most low birth-rate countries are first-world countries, and they generally want to only accept people who can contribute to their society and not be freeloaders to the social system. This means they need to filter out the people that come in, and being first-world countries, there is no shortage of people trying to get in. Sometimes they want low-skill, not-highly educated people just for the cheap labor, but not the person actually staying permanently, hence temporary worker visas. If a foreigner really wants to stay permanently, they then need to ensure that you are educated, able to support yourself long term, do background security checks, and make sure you agree to integrate as you mentioned in the OP.