It is said the unprotected left turn (right turn in left-hand drive countries like Australia, but I will write as an American here) is hard for autonomous vehicles (AVs). (Even ignoring pedestrians, which magnify the complexity if there were to be treated as full-fledged users rather than an after-thought.)
With an unprotected left turn there is ambiguity about whether gaps between vehicles are large enough for the AV to squeeze through safely, and whether oncoming traffic will yield to an attempt to cross, particularly as the wait gets longer and longer and the passengers in the turning vehicle become more and more impatient.
It’s hard for humans too, left-turns comprise a quarter of all pedestrian crashes. So why do we have it? I.e. why don’t we protect the left turn.
It is a matter of vehicle delay and storage space. On a one lane per direction road, or even a two lane per direction road, vehicles that are queued to turn could block vehicles that might otherwise go straight (or vice versa) when there is no turn bay and they don’t simultaneously have a green.
We could have a phasing configuration which gave each approach (North, South, East, West (N, S, E, W)) its own green time. In this case, if flows were more or less equal between left turns and through/right movements, this might be the optimal solution. But if flows were dominated by one or the other, then it would be less than efficient.
Alternatively, if we have turn bays (dedicated turn lanes) to keep vehicles out of each other’s way, we could have a configuration (N/S Through/Right, N/S Left, E/W Through/Right, E/W Left) which paired the turns. But turn bays use up lots of space that could be alternatively used for just about anything than temporarily storing cars.
And of course these could be mixed (N/S Through/Right, N/S Left, E, W) depending on relative flows.
But if the North flow > South or East flow > West (or vice versa), then these strategies will leave large gaps that could have been used by crossing traffic, but weren’t because the signal wasn’t timed for it.
With sufficient real-time information about flows, the signals could be adjusted to turn the lower flow approach to red when there are no vehicles approaching to protect the higher flow approach. This information requires knowing total approaches, but would be more accurate if the number on each turn (left, through, right) were also known, but this might be hard to discern simply by their location if the use of turn signals is imperfect, and there are too few dedicated lanes.
Update: We could prohibit left (right) turns. This is down in Moscow, so I understand. The left-turn ban at intersections is useful with low-rate flow turning left, assuming all left-turn vehicles are willing to do right turns several times to get to their destinations. But, this may impose a heavy burden of additional traffic on other road sections.
Or we could just have more roundabouts. These create other issues.