Late bus riders issue

Just after school, after getting on my bus, the bus driver was driving the bus off the drop-off area. A few seconds later, some students who ride the bus ran after it and a sister of one of their's urged the bus driver to let her off the bus to get her sister. The bus driver says "I'm not allowed to do that." and continues driving to the bus routes. After a few roads into it, before the first stop, the driver drives the bus beck to school and got one of the administrators to talk to her and her sister & her friend about the rules of bus riding.

I've seen this happen many times before, but I've also been wondering...
Is it really okay to leave the people who arrive late for the bus? Is it really a good rule to do that?

Personally, I think it's not. Anyone of the bus riders should be allowed
to get in the bus even after its departure schedule and the drivers allowed to let them do that.

 

The bus driver should have let the girl off the bus, a person can disembark at any reasonable point on the route (I think >_>). But, if the bus has left the stop and started driving then people start running there is nothing to make it stop. The driver has a schedule to keep to. If all bus drivers did that you would be complaing because buses would be later and journeys would take longer.

 

There is also a matter of time involved in the permission. As in, if a bus would be late for only one minute, should the bus driver let such-and-such let on or off?