Re: The embedded gear is often based on very low-power hardware
Shouldn't take months, considering the rate at which PCs can acquire randomness it might take a few hours. So start out using a weak key and then replace it after it has been running long enough to generate a strong one. Not perfect, but better than always using the weak key.
Alternatively, when first powered on they could connect to home base to get the initial key, and then replace it a few hours later. That prevents the weak key window, but I imagine some people would not be very comfortable with that.
Maybe some public organization needs to set up an internet accessible source of entropy as a public service, similar to how there are NTP servers as a public service...