This was the way my hometown traffic signals operated. People didn't wander aimlessly into intersections, however; there was always a tidy march either straight across the street or diagonally, which was called "catty-cornered." That's a term I haven't heard in years.

[It's a colloquialism for "catercornered." - Dave]

I remember doing this dance across the downtown streets of Baltimore in the early 50's. As matter of fact Mom could be pulling me across Lexington Street in this photo.

It's being introduced here in Adelaide, South Australia as the 'Square Dance' intersection. I don't know if it's been used here before, certainly not since I started driving in the '70s.

It seems effective to protect those pedestrians that seem to get 'simpler' every year from the drivers who were 'simple' to begin with.

I remember this system being in use at many intersections in downtown San Francisco when, in the 1954ish period, I'd accompany my mother on shopping trips. It was called "scramble" then, and a quick search finds that it's still the term where it's in use. If you can believe Wikipedia, there are still a few in SF and and in some other US cities. The disadvantage isn't about pedestrian safety, as vehicles on both streets have a red, but in the potential increase in vehicular congestion.