I also still find it kind of odd, but it's not like the light is doing nothing.
Typically, at least here in Germany, a crossing cycles between two states:
* Cars can go north/south, pedestrians can cross the east and west roads
* Cars can go east/west, pedestrians can cross the north and south roads.
The key thing here is that pedestrians don't cross the "active" direction, i.e. when cars are going in a straight line from south to north, they will never run into a pedestrian crossing the road in front of them. This is ideal, because cars going in a straight direction tend to go quickly, so we want to alternate fast cars and pedestrians.
However, obviously cars don't just go north and south, sometimes they turn. To turn, the car naturally needs to slow down, and also typically be more aware of their surroundings. Theoretically, this means that they are a lot more likely to see, and be able to stop for, a pedestrian crossing the road as they turn.
The argument then goes that this group of cars is slow and aware enough that they can share a stretch of road with pedestrians (unlike fast cars traveling in a straight line, which must not share a stretch of road with pedestrians). Which means that you could allow pedestrians to cross if (and only if) the cars that they would intersect with are slow, turning cars. The advantage is that you go from three states in the cycle (cars N/S, cars E/W, all pedestrians) to two (cars N/S + pedestrians E/W, cars E/W + pedestrians N/S), which improves throughput because fewer people need to wait.
In practice, this works for relatively small junctions with one or possibly two lanes, but three+ lanes become more complicated and need more states to handle the cars going left and right from different directions. But there is a thought process here about trying to find the right balance between safety and efficiency. As someone from the UK, I'm not sure I'm a fan, but some of that might just be not being used to it.