I think the answer to pedestrians versus cars is the same as for cars versus trains: grade separation.
Turn the sidewalks into elevated walkways. Or use pedestrian tunnels underneath the road surface. Pedestrian crosswalks are a money-saving measure, ignoring one of the many externalities involved in automobile manufacture. Cars simply should not be driving on pedestrian walkways, and pedestrians should not be walking anywhere that does not have a significant physical barrier between them and the massive objects moving at high speed.
Elevated walkways? Half my city doesn't even have traditional sidewalks today, who's going to agree to pay to elevate them?
Around my area, people don't walk for pleasure, mostly, they walk because they're too poor for a car and the public transit system is terrible. Forcing them to climb stairs (assuming they're even physically able; a fair number of pedestrians near here are in wheelchairs) to get out of the way of cars is a non-starter.
You only need to grade-separate the crossings. There are plenty of examples of pedestrian overpasses for busy streets. You can get around a big area in lot of major cities without ever crossing a street at surface-level, but as already mentioned, it is expensive.
(Though I can't imagine people being happy about going up and down stairs, escalators, or elevators every time they want to cross a street.)
The necessity arises from the car-drivers, so you charge them for the pedestrian safety measures, just like you charge them for the creation and maintenance of limited-access highways.
Without crosswalks, there is no pedestrian-crossing phase needed in the traffic signals, so separating the two types of traffic simultaneously makes cars faster and pedestrians safer. The question really is how much drivers would be willing to pay to shave that last minute off their commute.
If you look at projects like Boston's "Big Dig", the answer is that they are willing to spend quite a lot [of other people's money].
Some traffic engineers¹ argue that the problem comes from humans adopting the mechanical role of a "driver" who is entitled to seek the quickest route by a set of rules which they understand and adhere to imperfectly. Instead of trying to encourage everyone to pretend to be a robo-driver they emphasize returning to self-evidently confusing and complex environments which put the onus on the driver to negotiate.
Digging out extensive underground road infrastructure is very expensive. Ask Boston residents if they'd like to do a second Big Dig on a much larger scale to bury the streets.
Elevated walkways would be vastly cheaper, but still infeasible on any current budget. You would end up having to rebuild the lobby of most buildings to be on the second floor, and probably turn the first floor into parking. It feels like one of those utopian ideals from the 50s or 60s that came out before people started thinking about the money.
On the other hand, the downtown area of Chicago was raised up from natural ground level in the 1850s.
Seattle was raised in the 1880s.
A portion of Atlanta was raised in the 1920s. They actually did rebuild new lobbies on the upper floors, and a lot of the old storefronts are still intact down below.
i lived in boston during (the tail end of) the big dig and remember the excess costs were largely due to corruption and maybe some incompetence. look at how much nicer it is there because of it. i'd vote for it again in a heartbeat (with some better processes and oversight of course).
but yes, underground infrastructure is expensive (maybe the boring company will help drive equipment costs down), but we're a rich nation and we want nice things. i think we can do it if we want to. plus, it creates working class jobs and that makes the economy go 'round.
This was tried on a fairly large scale in Milton Keynes, a new planned city in the UK founded in 1967. The traffic grid is high-speed (and roundabout-heavy), and there was an extensive network of grade-separated pedestrian and cycle lanes.
The results are... mixed. Some people love the place, but the grade separated cycle paths are not popular. Well worth looking at, if this is an area you're interested in.
Umm, sidewalks are a separate right of way with significant barriers (parked cars)? Most train crossings are at-grade and use simple traffic lights. In congested areas, they install gates that prevent cars from barreling into trains.
You're thinking of sidewalks in a city. I don't know about elsewhere, but more populous places in Metro Atlanta have long sidewalks running between subdivisions and retail with no more than a small bump between it and the road.
Sidewalks found in suburban sprawl are purely decorative. Only the very unfortunate walk there because everything is miles apart from each other, making a car mandatory. Meanwhile, even super-dense cities, where walking is obvious, have to fight the ridiculous notion that cars deserve 80% of the street right of way and stupendously subsidized street parking.
No, sidewalks in suburbia are super useful for walking between houses. They're not useful for shopping or commuting, but they let kids walk to their friend's house to play. Not every trip is a commute downtown.
Underground tunnels have a mythos of danger surrounding them. Somehow a tunnel as long as the width of the road is supposed to be a hiding spot for a mugger.
Turn the sidewalks into elevated walkways. Or use pedestrian tunnels underneath the road surface. Pedestrian crosswalks are a money-saving measure, ignoring one of the many externalities involved in automobile manufacture. Cars simply should not be driving on pedestrian walkways, and pedestrians should not be walking anywhere that does not have a significant physical barrier between them and the massive objects moving at high speed.