How does immigration solve the issue. Once they become wealthier, their birth rate is going to drop, so you have to keep importing poor people from overseas to keep your GDP rising. Why not address the issue itself instead of trying to bandaid it.
Even if you can't reverse the population decline you can at least not make it a dramatic collapse and go through all the human suffering that entails.
The reason people don't have kids is not just the cost of doing so but the massive commitment it entails. People have more agency and mobility than they did before and they don't want to give that up. Importing people and ignoring that is printing more money to pay off current debts.