Note that area:highway=* areas complement highway=* ways but don’t replace them. The current generation of OSM-based routers is largely unable to route through areas, only around them. As long as the intersection is represented as both highway ways and a highway area, the classifications should be consistent to avoid confusion.
The pedestrian mall in the background of that photo would be highway=pedestrian, so if you map that as an area, it would be tagged area:highway=pedestrian. However, the intersection in the foreground probably should not be highway=pedestrian. That would imply that a pedestrian can loiter in the middle of the intersection, enjoying the right of way over cars, just like in a pedestrian mall or other footway.
The “Pedestrian crossing as an area” proposal calls for area:highway=crossing, but on the talk page, I’ve argued that area:highway=footway footway=crossing would be more consistent with other established tagging schemes. A crossing area is the logical extension of a crossing way, not of a crossing node.
There’s also junction=yes for indicating the extent of the intersection. This tag is kind of like your area:highway=junction suggestion, but it comes up often enough that I figure it has a better chance of taking off, for better or worse: