FYI, this is an American thing[1]. There's no jaywalker in Russian, for instance. Or French. If you know any other language that has a word for that, let me know.
It didn't even spread to the UK:
"In other countries such as the United Kingdom, the word is not generally used and there are no laws limiting how pedestrians can use public highways."
[1] https://en.wikipedia.org/wiki/Jaywalking#Origin_of_the_term
I'm not convinced that the pedestrian outside crosswalk omission arose because of U.S. car-centric thinking. I think if any software engineer working on the project was told that their autonomous driving system wasn't watching out for these pedestrians, they'd be horrified. In fact, probably many of them were already horrified at how poorly their system was performing in general, and yet management still deployed the software in actual physical cars.
Pedestrian crossings aren't provided on most roads outside of shopping and business areas - you simply have to cross at a safe point and try to be visible.
I really don't know about the US but I can't imagine it's that different: surely people need to be able to cross the road without being run down as an unclassified object.