The best bet for fragments of culture, beliefs, way of life, world view, sense of morality, genetic variations, etc to exist as an average person is to have kids and instill the best parts of those values into them as a child.

If you're fine with your people's history just disappearing from the world, feel free to never reproduce.

Sure, but like, that's not what we're talking about. OP says western society is "outsourcing the job of perpetuating the population," as if there is some shirking of responsibility going on, or we all need to care about this for some reason. That's macro-level, not the personal choice to have children or not. No one is asking them to do that, so it's unreasonable to foist responsibility back on western society and then shame them for not fulfilling that responsibility.

Why is maintaining the human population at or above present levels something that so obviously needs to be done?

Probably to fund Social Security as life expectancy increases.

Maintaining a stable population in the steady state is something that needs to be done for society to continue existing. You can decide that, okay, maybe the target should be half the current population, but that just means that within a generation, those people in LA need to be having twice as many kids as their parents, which doesn’t seem plausible to me. Whatever the target is, the lifestyle of American secular whites (where the TFR is around half the sustainable rate) can either only be temporary, or must be propped up by immigration that only exists due to accidents of history and colonialism.

I’m only here with my three kids because the British colonized the country I’m from. The Latinos in LA—who are doing the grunt work of society as well the work of raising the next generation, while white people have dogs instead of kids—are only there because the Spanish were worse colonizers than the British. Secular white people tell me how wonderful their permissive, individualistic values are. But it’s like saying how great a job a government is doing when they’re running massive, unsustainable budget deficits. A value system can’t be “good,” in my view, if it can only exist because of an immigrant servant class.