David Reevely does a pretty good job of explaining the perils of interlining in the above link. However, interlining really isn't the biggest part of the tardy bus problem. Recovery time is what kills the schedules. It really doesn't matter whether the bus is interlined, because the late run stuck in traffic will be late for *whatever* run it is scheduled to do next. Whether the run is the same route number or not, somebody is going to be late.
Recovery time is the time between where a bus finishes a run and starts its next run. If a bus is consistently getting bogged down in a part of the city, then planning should increase the recovery time allotted on a run and begin the next run at a later time, or send an "extra" bus to fill in for the late bus. Either option costs the city money, as you have two buses covering the work that was allotted to one bus.
The solution for the customer is increased recovery time between runs for certain buses, or more "Extras" on the road to cover the scheduling errors and unforeseen circumstances.
It's all about performance expectations in the planning department, and the never ending quest for efficiency. As demonstrated by David Reevely however, efficiency sometimes comes at the expense of good customer service.