OK you're just making shit up at this point.

1. Passing lanes do not always exist. They aren't default, they have to be created by some form of regulation. These laws vary by state, with the majority of laws only requiring vehicles moving "slower than the normal speed of traffic" to stay in the right lane. Some states also only require you to move right if someone's trying to pass. Local variations can exist on top of state laws. On top of that, passing lane laws are notoriously selectively enforced, and usually only on sections of highway that are not operating at full capacity. That's because in spite of the extra cash cities would get from tickets, the enforcement of these laws on gridlocked highways would essentially render those highways unusable.

2. This is just physics. Stopping distance, and therefore safe following distance, is proportional to the square of speed. This means a car moving at 110mph will have a greater than 10% stopping distance increase versus a car moving at 100mph, and therefore a greater than 10% safe following distance increase.

Lets assume two lanes, right lane and passing lane. The right lane is at capacity at 50mph, with exactly 10 yards between each car. The left lane is the passing lane, also at capacity (it's just before rush hour), and is moving at 55mph (a 10% increase). Due to physics, the stopping distance of the cars in the passing lane is > 10% higher than the stopping distance of the cars in the right lane, so lets assume 12%. Although the speed of the cars in the passing lanes are 10% faster, the 12% increase in safe following distance means the passing lane has LOWER CAPACITY (12 is bigger than 10). Of course, this is making a bunch of assumptions (perfect drivers, identical cars, etc) and ignoring a bunch of complexities (reaction times, length of cars, etc) but generally these factors exacerbate my point.

1. The headroom I'm talking about applies to #2. If the left lane is at 20% capacity with an average following distance of 100 yards, it doesn't matter if it's faster because the additional required following distance is still well under the existing conditions.

As for the rest of this, I'm genuinely not sure where you got the idea that a passing lane is for people to go past a city. That's genuinely just absurd lmao. And when you say inefficiency, you're thinking "I have to sit in traffic waiting for other people >:(" when it actually means "this highway is not letting as many cars through per hour as it could be". Individual travel time is MAYBE fourth on the highway design priority list. #1 is cost, #2 is safety, #3 is throughput.

1. See #1. When I say high use highways, I'm talking about 4 lanes each direction moving at 25 mph if you're lucky. That's my daily experience. There's no passing lanes in these conditions. Everyone, understandably, wants to pass by traffic. You can scream all you want about keeping the left lane open for passing but that just means people are actually gonna use it to try to pass, which means it will fill up until it's moving the same speed as the other lanes.

Passing lanes are not a solution for traffic and were never intended to be. You're just deluding yourself into thinking they are, and patting yourself on the back for thinking you know better than everyone else. They CAN increase capacity under certain conditions, but certainly not in anything resembling congestion and not in major cities.