The waiting time paradox: why is my bus always late? (2018)

There's another thing that happens with busses that makes it worse.

The further behind the previous bus a bus is, the more people will arrive at the bus stop. The more people there are at the stop, the longer the bus has to spend picking them all up and selling them tickets etc. Therefore the delayed bus will tend to experience more delay. The bus behind them will have less people to pick up, so it will spend a shorter time at stops and tend to catch up with the first bus, so the two busses are dragged towards each other.

This phenomenon consistently happened to my college bus system, but on an even worse scale. The main bus line did a loop around campus, which took ~20 min to complete and buses scheduled every 5 minutes. In reality, you got a caravan of 4 busses arriving every 20 minutes, with the first one totally full and the last practically empty.

When I was a teen in Calgary the transit agency was really good at dealing with issues like this during peak periods. They would pair or triple busses together and alternate stops. If someone requested the stop the drivers would radio to coordinate. Sometimes both buses would have a requested stop, but they would work together so only one bus allowed new riders on. The non-loading bus would quickly drop off passengers and leave while the other stayed behind to handle new riders. Nearly all the stops had dedicated out of traffic space for the bus, so the leap-frog maneuver was really simple. A small amount of low cost infrastructure and some operational cooperation enabled much better service.

Another simple strategy that I've seen is simply for the loaded bus to allow the empty bus to overtake it and go on ahead (and just stay ahead).

That sounds identical to what the Calgary busses do? You'd still need coordination between the busses to know when the loaded bus "wants" the empty one to overtake it.