This reminds me of the book The Goal by Eli Goldratt. It's fictional, but there's a story about a boy scout troop that goes on a hike, and there's an overweight kid named Herbie who hikes the slowest. The troop leader teaches everyone that the entire group as a whole will reach the top faster (and stay together) if they keep Herbie in the front.
When you have a bottleneck step in your process, the whole end-to-end process will run the most smoothly if everything else matches pace with the bottleneck.
We would rotate who got to be at the front on long treks (Philmont). As the 'head' of the snake, you take ~100 paces or whatever, then you step off to the side of the trail until the entire group has passed you. You are now the 'tail' of the snake. The new head of the snake then steps off after 100 paces and everyone passes them etc. The side benefit is that everyone gets to take short rests as they wait for the 'body' of the snake to pass them.
Did you work at Amazon? It's a cult classic hazing ritui there. Managers tell reports to read it and then joke about terrible a novel it wrapped around a few cute stories like that one and the paperclip passing game.
Ha! No, Microsoft--I was in the hardware supply chain group for a while, and The Goal was a common conversation topic there. I heard a few people call process bottlenecks "Herbies."
The point is that within the boarding process, the slower (elderly, disabled, traveling with children etc.) people are the bottleneck, and letting them board first actually makes the boarding process take less time. The pilot can't even start waiting to get permission to fly until after everyone's boarded.
When you have a bottleneck step in your process, the whole end-to-end process will run the most smoothly if everything else matches pace with the bottleneck.