You say you've observed it, but it doesn't make any sense. If you go 5mph slower than the speed of traffic, you will continuously open up a gap. You never need to slow down farther than that. The cars merging into the gap wouldn't be merging if your lane wasn't faster than their lane, so there's no reason you would have to slow down even farther. What you perceive as repeated slowing down will only happen if you sped back up to match the speed of the car in front of you after opening the gap.

I don't think you've considered what you are saying. You're not describing a gapping strategy, you're just describing a slower driver (i.e. slower traffic). There is no question that a car consistently driving slower than ambient traffic speed is a net drag on overall throughput. In any single lain of traffic all cars are bound by the slowest car. If you drive 5 mph slower than the car in front of you then the car behind you must drive 5 mph slower still to continually produce gaps behind you. As the video illustrates introducing a slower driver is one of the things that creates phantom stop signs.

Of course you must maintain speed. The point of a gap is to allow for adjustments without the hard breaking that would create a phantom stop sign. That is the overall intent of the system. Move the most people as expediently as is safe from point a to point b. The best way to do this is to avoid speed differentials, being slower then ambient traffic speed creates a speed differential.

That's not true about the second driver behind me, because people are not pulling into his gap, because his lane is going 5 mph slower than the other lanes. So he establishes it once and is fine.

This is more of a thought experiment to show that you never have to keep slowing down to zero even if for some reason people continually enter your gap. I barely observe people entering my gap at all in practice, because all lanes are generally going the same speed so there's no benefit to it.

Because you insist on the gap, your lane is 5mph slower than the other lane (because people pull in front of you after passing). Assume the other lane is doing 50 (65 mph speed limit, but there is congestion).

That lowers the throughput (number of cars that complete a trip in your lane) by ~ 10%. Also, the faster lane is now probably moving closer to your speed behind you than the 50mph you observe (because you are causing cars going 45mph to cut off cars going 50mph that lane).

The arrival rate of cars won’t change because you chose to go slow. So, if the road can handle 10,000 cars per unit time with normal congestion, it can now handle ~ 9000. That means per unit time, there are 1000 new cars sitting in the stop and go backlog that you single handedly created by creating the gap.

This has been shown time and time by traffic simulations. It only takes a small handful of slow drivers to create massive backups.

Also, the number of traffic fatalities is proportional to the difference in speed between the fastest and slowest car, so, statistically speaking, by being the slowest car, you are murdering people.

The reason I am going 5mph slower in this thought experiment is because a continuous stream of cars is merging in front of me from the other lanes. (What the OP called the 'pathological case'.) They are the reason the lane is slower, and because they are not in the other lanes, those lanes will be 10% faster.

With the pathological case being so benign, the real life experience is even better. You might get a car moving in front of you once a minute, and usually a few seconds of slower accelerating or coasting is all you need.

To me the thing that really slows down traffic is people not moving left to let onramps merge. I think that's because they are afraid of missing their exit because no one is leaving gaps.