That's silly. Driving in America at least is a quasi-right: while not technically a right by law, as things stand the economy and much of society in the country would collapse if most adults were not able to drive. But at the same time driving is not natural and definitely represents real danger. So the law reflects a balance between these two competing interests, with safety concerns slowly getting pushed harder over time. Driving requirements are relatively forgiving, and removal is taken seriously. But there are a lot of laws and thinking around how to improve safety. The licensing process has become more of a ramp too, with many (all?) states having increasingly graduated licensing and some starting to have rechecks needed for the elderly. Licensing for non-necessity driving (commercial vehicles, motorbikes etc) sees a significant spike in requirements.

People very much care. In highschool I had a good friend hit and killed by a drunk driver while they were walking right near school, and I would strongly resent any putting down of how devastating that was for the family and our group. But "individualized mechanized arbitrary point to point transportation" is also very much critical, and with current technology that means "a human driving". It's very unfairly glib to impugn that society isn't trying to balance here. What is needed to radically change the status quo is to finish the car technology so that a human is not needed. Once that is the case and manual driving becomes a fun luxury I expect we'll see licensing requirements and training increase a great deal, looking more like what professional motor racers do. The converse from a privacy perspective is that no, many people will not bother to carry drivers licenses with them anymore, nor will they need to.

Generalized authentication is and should be an important role of government, so some form of ID will still matter. But in terms of needing to have it on you? No, I do not think that legal requirements around that will change. The "true purpose" of a drivers license is in fact trying to have some minimum level of competence and personal responsibility attached to the act of personally controlling a multi-ton pile of metal moving at high speeds.