My take is that saying the problem is birth rates is misguided. Surely we have enough labor to provide for the elderly, why can’t our economy be structured to get this labor to the people who need it?
Well yeah, because it's difficult, taxing, often traumatic work that pays the same as any other nursing job with a higher QoL and social status. And even then they're pushing out all the actual nursing staff that pays well in favor of MAs/CNAs who get paid like shit.
I personally don’t think wages always correspond to how essential a job is, but for the sake of the argument let’s pretend that wages match the necessity of a job, its difficulty, educational requirements, etc.. In this case, I’d expect that we would see people move to jobs that are more essential than their prior job. I think this is more complex that just “poaching”.
I really don't mean to get into the nitty gritty details - I'm not an economist and I'm not providing solutions, just stating what I see as the problem. I believe that we have enough resources, and there are issues getting those resources to where they need to go.
Example: Assume we do have a shortage of elderly care workers. Why is this the case? Could this be fixed by increasing their wages? Then that implores the question of who is paying for these increased wages, which is the question I'm not answering and I don't know enough to answer.
I just don't really believe that keeping the birth rates high is the answer to this economic problem. It might be a solution, but it's more of a band-aid than truly facing the issue. If you have a inefficient engine you can either figure out how to produce more gasoline (babies), or you can figure out how to produce a more efficient engine.
A truthful ad for working in an old folks home in the US would be, "slightly over median wages, but with inflexible and unreliable schedules, rampant industry wide exploitation of workers and their rights, likely multiple ownership changes of your place of business, caring for potentially deranged and violent individuals, high non-refundable monetary investment up-front, no guarantee of residency availability"