>1. We have democratic checks and debate now, regarding this issue.
Not functionally, consistently, or meaningfully. Many of these companies have learned to how to ingratiate themselves to party machines in the markets where they operate, such that this decision-making is almost entirely excluded from public check or debate. Others, like Uber, willfully break laws with little consequence, for much of the same reason as the above.
>2. I see no evidence that "massive, publicly-funded investment" would achieve this technological goal faster or better than via capitalistic means. Do you have any?
As someone else pointed out, its not about faster but more safely. But the whole technology that these companies are building on top of was arrived at by this kind of public research to begin with:
https://en.wikipedia.org/wiki/Self-driving_car#History
>3. Lives will be lost regardless of how the tech is developed. Surely this is obvious. So what are you even talking about?
That private companies not be the nearly sole arbiters of what lives are worth sacrificing.