Third world families beget more families than European families. If your family sponsors third world family, then in one generation, your children’s families will have to sponsor more than one third world family in order to keep up. Third world families beget their next generation in a shorter period than western families. If your family sponsors a third world family, your children will have to start sponsoring third world families (plural, each) before they themselves have started families, if you and they are to keep up.
I just don’t understand why people suggest solutions that simply cannot work. They want your money. They want your freedom. But I don’t know why.
I think you just simply haven't thought it through enough. If you read some of the replies that precede your comment you will find some interesting thoughts that indicate that it might very well be possible.
It seems quite clear that whatever it is we are doing now certainly isn't working.