From a purely traffic load perspective, the whole "fast lane" thing doesn't make a huge difference, and the aggressive obsession with it is actually a big part of the psychology which creates traffic in the first place. Traffic capacity is generally optimized when everyone is traveling close to the same speed and has enough following distance to safely maintain that speed, which is why speed limits are set for the slowest road users. Just in general, speed does not increase road capacity beyond a certain fairly low limit because it requires dramatically increased following distance, or in the absence of such responsible behavior, it massively increases the frequency of traffic disruption.

The worst case is a few people traveling much faster than the slowest road users, as these few users both take up more space, and cause more disruption. The "fast lane" concept is rooted firmly in an unfortunate behavioral reality and has basically no real scientific basis beyond that. Even if you had perfect robot drivers with perfect reaction time and the ability to see far ahead of themselves, the critical capacity speed only increases slightly because the maximum stoping distance is still limited by rubber and asphalt.

You have demonstrated why fundamentally humans suck at driving and this problem is unsolvable.

Not because you asked the question but because it's not intuitive why.

So long as this has to be explained to anyone it can't be solved.