At first glance this does sound like the Nash equilibrium outcome in a situation where every country's unilaterally optimal strategy is to aggressively increase their domestic populations primarily through reproduction instead of engaging in a zero-sum competition to attract immigrants. But this implicitly symmetric prisoner's-dilemma-style model doesn't map cleanly to our reality, where initial conditions are asymmetric: wealthier (usually western/imperial) countries who don't have strong xenophobic preferences can more easily attract and assimilate immigrants than poorer ones more likely to experience net emigration, which would have to outbreed the wealthier xenophobic countries (on a per-capita basis) to achieve the same ridiculous objective of tripling their population sizes.

I haven't read the book (because why would I?), but Matty Glacier is in all likelihood aware of this asymmetry between the imperial core and the ex-colonies, and if he isn't a complete knucklehead would advocate for the US to focus on tripling its population size (again, still a ridiculous objective) by continuing to attract immigrants and beating other countries at the zero-sum migration game, rather than by attempting to outbreed (in absolute terms) the naturally-much-larger Chinese and Indian populations while tightening border security like an openly racist piece of shit.