We can't get rid of cars and streets. That cat is over a hundred years outside of the bag. It's moved on, had it's own family, and died.
Jaywalking as a punishable offense makes sense to me at least. The level of punishment is often excessive certainly. $250 fine for stepping onto the street is far too much for a first offense (but perhaps for a habitual jaywalker it makes sense). Hell, I'm guilty of doing it a lot in my exurb area. However, when I do it it's because there's 2 miles between posted crosswalks and I make sure I can cross safely before trying. There aren't enough crosswalks - certainly.
Jaywalking laws create important predictability. I can assume that the average civilian is deterred by jaywalking law enough to not randomly step out onto the street at will. This means I can anticipate them only at crosswalks and intersections. You're already busy dodging drivers distracted with doing anything but driving (makeup, listening to podcasts, eating, reading a book, etc). If we didn't have these laws the risk to driving would be much higher. Many people think humans stand no chance against cars, but one errant jaywalker going through a car window can kill everyone in the vehicle given sufficient enough velocity. It's important to remember a 45 mph impact on a ~125-200 pound human carries with it tremendous momentum. Assuming they don't go through the car window, that same flying body can do lethal damage to law abiding people walking on the sidewalks.
The UK doesn't have jaywalking laws. I understand that. But the UK is far more "walkable". The US is by-and-large not. Especially as you get into "normal" towns and not major metros like LA and NYC. I would be willing to agree jaywalking laws need to be done away with if the US was more walkable.