Yes, I understand all the functional advantages, and I'm 110% onboard with that idea. I came here to learn about the actual hardware. How will this biohoohah login work when I connect with my PC? It sounds like I'm going to have to buy some expensive peripheral device.

Once upon a time, there was this thing called a dongle. https://en.wikipedia.org/wiki/Dongle
Second paragraph, where it talks about their initial use as a hardware solution to DRM.

In order for this idea to work and be secure, it's going to have to be prohibitively expensive. And for that reason alone, I don't think this solution is going to be practical.

And as for my "basic understanding of how private keys in crypto work", I believe I learned the fundamentals of that when PGP was new back in the 1990's. Ahem.