I'm assuming here just based on experience, but...you don't just go to your seat and sit down, you have to put your bag in the overhead bin, which takes some "aisle time".

in back-to-front, a line forms as you are waiting for people to store their bag. one person can take up [block] 3 rows of seats while he is fiddling with putting his bag overhead.

in random seating, people all over the plane are storing bags at the same time, instead of just 1 or 2 people.

I wonder what the percentage is of those delaying the line due to their slowness vs. the need to search out space.

The most aisle time I've taken on any flight might be 10 seconds, though most of the time it's zero since I prefer to store my carry-on below the seat when I can.

Instead of thinking of the problem as "how to get the group of people to sit down the fastest", the problem should be thought of as "how to get the group of people to put their bags away the fastest" (or at the same time).

From the simulation it looks like the bottleneck forms because each person takes a minute to put their bag away. So if you have 1 person in the last isle putting their bag away they are basically blocking the entire plane.

With random you get random people who can access the overhead compartments all over the plane which helps increase the number of people simultaneously putting bags away.

In my mind, it's the difference between having a singular thread of execution vs multiple threads.

The people in the aisle are units of work that need executing. In back to front, only the unit that is right at the front can actually be completed since only she is blocking the people behind her, who are in turn blocking the people behind them.

In a random setup, say the first person goes right to the back of the plane, there's every likelihood that the person behind her is not sitting next to her, which means that 2nd person can immediately reach his seat while she does the same..

Multiply this a good few times, and you'll see that a number of people proportional to the total number of passengers will always be getting seated at one time instead of just 1 or 2..

Doing it in blocks seems wrong. Instead, you should have 10 people board the plane in order of their seating, back-to-front, but have those 10 spaced evenly over the plane, so they have at least one row between them. They're all spaced out so they don't interfere with each other.

Then again I avoid airports these days because of the TSA.

Also back to front is usually done in cohorts - not a truly sorted stream of people. You end up with the people in seats 36 waiting to get around people in seats 32 just because they are in the same group.