There's no problem with grids or wide roads as long as there is infrastructure in place for pedestrians. Bridges can allow people to cross over wide streets/traffic without having to wait for a light for example. Tunnels can be an option as well. Grids can really help a city be more walkable since it becomes dead simple to navigate and you aren't wasting time on long winding roads or labyrinthine paths which increase the distance between two points and make it easier to get lost.
Infrastructure for pedestrians would be you cross as soon as you get there, cars wait. Bridges are not pedestrian infrastructure they’re “cars are the priority” infrastructure, “cars mustn’t be delayed or inconvenienced, pedestrians can be” infrastructure.
None of the world's great walking cities heavily uses bridge crossings like that.
What do work for pedestrians is a network of smaller roads that you can "just" cross safely without waiting or taking detours. Basically, a few big roads you cross once in a while and the rest being smaller roads where cars are forced to go slowly.
When you consider that drivers are generally wealthier (because they own cars) and the pedestrians are breathing car exhaust and tyre dust while working their lungs harder climbing to give cars the priority, listening to car noise while drivers pass in low effort comfort, the mild unfairness of it is more starkly contrasted.
Ideally good pedestrian design would tempt people out of their cars because walking is so quick, convenient, cheap, pleasant, interesting - with shade and shops and short distances and quiet clean surroundings. Big steel bridges don't contribute to that very much. [Have you seen how often Americans comment on the price of gas? Yet what people campaign for is the government to lower the price of gas, not for the government to make life without cars so pleasant that cars are not a necessity. What sense does that make? Most living Americans have never lived in a walkable place, and have no film, tv, or cultural reference for one to use for a basis for such a campaigh - maybe Disneyland (which visitors tend to love)? 120 years ago everywhere was walkable because there wasn't much other than walking. 70 years ago places were bulldozed for cars. Now multiple generations have grown up and lived their adult lives with car dependent urban design].
There were severe injuries or deaths every single year when students would cross the road late at night and a car would be speeding at 60+ mph. They eventually installed a puffin-style crossing, which was much better.
The solution, especially in built up areas, is to keep cars from causing problems for pedestrians rather than trying to stop pedestrians from causing problems for cars. Perhaps the cars should be relegated to a tunnel so people don't have to be near them instead.
To be walkable a city needs to be quick to walk between destinations and pleasant to do so.
Most US cities are too spaced out, require waiting at each block, or are not all that pleasant for walking.