It seems like the right word. Hedonism doesn’t imply debauchery. It’s just prioritizing pleasure.

It’s a hedonistic choice to forgo children in order to enjoy the pleasures of an unencumbered lifestyle. It’s also a personal choice (though I would not say it’s straightforward for most).

It's always invoked as if that makes life shallow - if avoiding pain (raising kids) is hedonism, then yeah I'm a hedonist. I'm not going to self-flagellate to appease society's desire for workers. Bad assumptions about demographics aren't a good reason for people to procreate, just to prolong a scheme that can't hold.

Does "coping" in this situation mean having 75% of any western countries young population foreign born and erasing thousands of years of culture and history?

Now in addition to preserving the economic order, people are responsible for preserving culture and history? That's too much to ask for. Cultures evolve. Our children might not choose to follow our culture. Even within any given western country, people disagree on what the indigenous culture consists of. My country has been described as being in the midst of a culture war.