I don't think that doctors and nurses are the limiting factor for home care, but rather home health aids and CNA's - basically people that check in on patients around the clock and make sure they're kept clean.
In the context of the US system, your original comment is just completely off the mark. Our healthcare system is universally terrible, independent of the cost ("not my job" at every level). Consigning a elderly person to that system is basically the last thing anybody wants to do, hence the focus on dying at home etc.
I can't speak about Germany's system. But it's worth remembering that money is not equivalent to resources, and that spending an imprudent amount of money on elder care right now doesn't imply that there won't be resources left for you later. Whether the system is "burnt to the ground" has more to do with if the institution is destroyed or hollowed out, rather than how much it costs.
And to be clear: It would be great if we had enough doctors, nurses and resources for everyone to die in their own home with all the amenities of a hospital specialized to end of life care but hat is practically impossible. And I don't mind socializing healthcare. On the contrary, I think it's a necessity for any civilized country. But given the aging societies of basically all western nations I would bet all I own that by the time I need end of life care, at home care with private nurses will become the privilege of the super wealthy.
Here in Germany, the system is already essentially collapsing and it's not even a money issue, it's a personal issue. But sure let's burn it all to the ground for the now-dying so by the time my generation needs it there's nothing left.