The politics around allowing immigration are complex and controversial though. Som e people will fight tooth and nail to prevent more of the "others" from coming into their country. I'm not just referring to the US and Europe.
Look at Japan for example. Immigration has been touted by Western think tanks and pundits as a solution to their demographic problems, but instead they've chosen to go all in on automation and robots to attempt to solve it.
I expect Korea to follow the same path. Probably China too. A lot of East Asian countries that are at the bleeding edge of the demographic bomb place extremely high value on population and cultural homogeneity. The West would probably label that as racism.
I would imagine such aggressive measures (i.e. forcing of anything) would occur first in a certain other countries before it happens in the West - if it ever does. I would also not be surprised if the West would implicitly choose to implode first before sacrificing an iota of "freedom and individuality".
Outside the West, I also would not be surprised if some countries/cultures would implicitly choose to implode before sacrificing their homogeneity.
America is never going to "force" people to have children, but it may ramp up transfer payments to those who do. The Child Tax Credit was a big part of the Biden agenda, for example. So is, AFAICT, subsidized daycare and such.
(If more aggressive payments by other countries are any indication, this will have approximately zero effect on people's decisions.)
In typical EU cities the default housing option is a small 2 bedroom / 1 bath flat. That makes it awkward to have more than one child. Admitting more immigrants further increases competition for very limited housing supplies. Building more housing in those cities would probably be a good idea but realistically it's not going going to happen on any large scale.
Wouldn't it be a lot simpler to just allow more immigration?
I mean, there are plenty of young, able-bodied, english-speaking people who'd like to move to rich countries.