That's where it's important to consider the often sprawling nature of suburbs and how they're inherently unwalkable. While that is definitely a problem, it seems to be a sprawling problem.
Its not a suburb or sprawl problem. It's a car problem.
I now live in Manhattan, the most densely populated chunk of the US. Any time I walk somewhere I spend about half the time waiting for lights so that I can safely cross a street.
Well, I don't disagree at all, but would argue that it's kind of a circular dependency problem. Sprawl would exist without cars to be sure, but cars make it much easier to expand, which increases dependency on cars, which supports sprawl. Then the people who have moved outward use their cars to work in the city because there's nothing in the suburbs and a poorly designed city (or one that is dependant on the people with cars) prioritizes that.
Well, suburbia started becoming a thing long before cars and comes from the Greeks. However, I don't think the kind of cities you see today would necessarily have expanded so far without cars. They are not a book to cities or density from what I can tell.
As someone who walks in Manhattan, I see where you're coming from, but my experience differs. Specifically, 99% of the time I'm walking in Manhattan, I'm not trying to get somewhere on the same street or avenue I started on, so I can turn and walk along whatever block to avoid the lights. Plus (at least in the 40s), there are plenty of subway entries/passages where you don't need to pay but can pass through to get underneath the street - and buildings you can pass through as well. Of course, figuring out this maze is half the "fun" of walking in Manhattan.
