First of all, I work near a multi-lane roundabout; and your image is spot on for how traffic flows there every single day. While definitely not the most efficient; it is very realistic.
The main problem that Cities Skylines has (in regards to your question), is that you cannot control lane usage. By adding an intersection to an otherwise straight multilane road), the existing lanes will be divided into straight/turn left/turn right lanes.
A simple example: Make a 4 way intersection. 3 of the roads are two-way 2-lane roads, and the other one is a two-way 6-lane road.
If you look at the lanes of the 6-lane road, you will see that the three lanes are now changed into a turn left/go straight/turn right setup.
It's a nice system. The logic behind it is pretty okay. However, it does not take traffic flow into account.
Continuing our example; suppose that 95% of traffic (coming from the 6-lane road) will turn right, maybe because that's the entrance to a huge industrial zone.
At no point will the game change the distribution of lanes to match the traffic flow.
What you might want to do is have the two rightmost lanes be "turn right", and the leftmost lane be "turn left/go straight". But in the vanilla game, that is not possible.
This is where the answer ends (sort of). It's simply not possible, unless you find a mod that does exactly that. But I'm not sure how well the AI would handle custom lane assignments.
Some things to consider
Referring back to your diagram; I also have to admit that this problem is somewhat unavoidable.
Let's say you want the red car to stay in the inside lane of the roundabout, and then use the leftmost lane of the exit they are taking.
- A blue car arrives (as per your diagram). It will take the first exit (the same as the red car). Now, with your proposed solution, there is no conflict because the cars are on separate lanes at all times. Problem solved!
- Another blue car arrives. This car will take the second exit (where the red car originally came from). Regardless of whether the red car uses the current path or your improved path, they have to cross eachother at some point. Your proposed solution offers no fix for this scenario.
The solution you mention, while it does help in certain cases; does not work as a global solution.
This problem you address is inherent to multilane roundabouts. If a car is expected to merge to the inside lane, you logically also have to allow it to merge back to the outside lane.
Think about it like you're the driver.
- If you are on the outside lane of the roundabout, you can always safely take an exit, because no one is driving on your right side. It's the safest option.
- Somewhat obviously, you should not suddenly brake when you are on a roundabout, to prevent accidents and not hinder the flow of traffic. This is even more important when you are on the inner lane (fast lane) of a roundabout!
- If you are on the inner lane of the roundabout, when you take the exit, you cross the outer lane before reaching the exit. If there is a car in the outer lane (that is staying on the roundabout, not taking this exit), then you run the risk of a collision or at the very least a hitch in the flow of traffic as one of you has to brake. Especially on roundabouts, unexpected braking can have disastrous effects for the flow of traffic.
- If you are on the inner lane of the roundabout, and the exit only has one lane, then the problem gets even bigger; since you now risk a collision (or unexpected braking) for any car that is in the outside lane, even the ones that are trying to take the same exit as you!
Your question and proposed improvement focus on the most efficient traffic flow. However, that is not how human nature works.
In the the driver's interest of personal safety, merging to the outside lane is preferred because it completely dismisses the risk of a collision (with a car that is also on the roundabout). And even then, it also improves traffic flow since it prevents unnecessary braking (which can be done either to prevent an imminent collision, or as a preventative measure because you're aware you're performing a dangerous maneuver).