As far as odd times (3am, for example) and odd locations: Yes, the government should include these. I've worked many jobs that would fall outside of normal route times at night (when I've had access to busses, that is). Weekends, late nights, early starts. These jobs range from nurses aides to pharmacy workers to fast food to retail to factory work. Many are low-paying, but some aren't.

If people cannot get to and from their jobs, especially folks working low-paying jobs, in a timely manner, it works against the goals of public transport.

Now, there are other good points to having odd hours: Getting drunk folks home, enjoyment of city life when city life is happening, and so on.

As far as the competing companies, they probably would bid to run the bus system in an area for x years. Overlap might be an issue otherwise.