For one thing, it would be incorrect for an empty bus to pass a full bus - a full bus can't take any more passengers, and the people who don't fit on the full bus would have to wait even longer, for the next bus again.
Secondly, people get off at stops, not just get on. The bus that overtakes won't get a big lead, because it probably has to stop anyway. It can only leave when it looks like the front bus is going to fit all the passengers.
Thirdly, the bunching that has already occurred (to make it possible for one bus to overtake another) means that the bus stops ahead have far more people at them. Instead of merely bunching together, one full bus followed by one empty bus, you'd have two fairly full buses leap-frogging one another.
The only way get back to a situation where the buses are on opposite sides again, minimizing variance in bus wait time, is to have a bus pause when it gets too far ahead of schedule.