It would likely be difficult to buy a car without it, and obviously you could not rent it (yes, code and blabla, it's just a proxy for it).
> Have you ever applied for a library card?
Yes, and in fact they were pretty fastidious with validating that I lived in the area they serve (that might be because I have a funny accent, but still). I don't remember how I managed to get it, eventually - likely with the usual utility bills, which here work exactly as ID would, as long as you have a pair of them. Their use for this is extremely problematic.
Did you definitely mean this? I have never had to present a driving license to buy a car. I don't see the link; the license isn't to own a car, it's to drive one. Unless you're thinking of places where one does need a license just to own a vehicle?
Have you ever applied for a library card? Most libraries will give you one without any verifiable form of ID. And the card itself certainly isn't ID.