If you suggest "shall we tax childless people" and frame it like that, very few people would support the idea.
If you suggest giving people who have had children generous tax credits to help compensation for the costs of raising children (and foregone career opportunities), a lot more people say they are OK with that.
Yet any kind of benefits or tax credits for parents are likely to be paid for by higher taxes by everyone else--ie, those who have never had children. It amounts to something that is basically very much like a tax on childlessness, it's just phrased in a less provocative manner.
Most countries will probably end up doing some version of this, IMO. They will find "nice" ways to frame it, rather than saying "Childless tax," but it will effectively amount to the same kind of thing.
I'm not particular pro or anti immigration, but fertility rates are falling really sharply all over the world, including the countries where many immigrants might traditionally have come from. Already, countries like Mexico, the Philippines and India are probably just slightly below replacement rate. Much of Latin America and Asia fell below replacement quite a while ago. Fertility has fallen more slowly only in sub Saharan Africa, but the % of sub Saharan Africans with the sort of skills we need in a modern developed country isn't very high (and those sub Saharan Africans who are skilled will be badly needed in their own countries). There is no easy solution to all this.