Cities need to prioritize walking, biking and transit. What this means is that, these modes of transportation need to be made safer and faster. Currently walking through a major city is bogged down by the number of intersections you have to wait at. One idea would be to make intersection movement faster for pedestrians and transit during all hours except the morning and evening rush hour, during which vehicle movement should be prioritized to get cars off the roads as quickly as possible.
That's the functional definition of "rapid transit": faster than a car. This can be because the transit is so fast, or because the car is so slow (gridlock/rush hour traffic).
If you have transit that's faster than a car, and it goes where people want to go, you use the transit. A great example is Chicago's EL. You don't want to drive a car around downtown Chicago, you want to take the EL.
With the exception of areas where it's impossible (NYC) IME the majority of pedestrians and cyclists simply do not care about the crosswalks/laws/etc. Jaywalking is constant as is crossing in the crosswalk against the signal.
What I'm saying is outside of structural changes to the roads themselves (like you mention, eliminating some intersections) I don't see much change happening.
The very concept of jaywalking or dedicated crosswalks is a symptom of the car-first mentality.[0] If pedestrians and cyclists had the right of way as they should, this wouldn't be an issue.
Crosswalks are awful. Outside of the ones where there is an actual traffic light, they are always placed in terrible locations. Moreover, they are just about the worst place possible to try to cross a street. I've been doing a lot of walking around the medium sized town I live in the past year, and I've had to get very good at looking away from the road when I want to cross, otherwise vehicles that have a quarter-mile of empty space behind them will come to a stop, and make me feel like I have to rush across, when they could have just kept going, and we would have both been able to go about our business at our leisure.
