You want to set a precedent
Especially if you are public service agency, like the EPA, you might want to set precedent that businesses won’t get away with polluting, or otherwise acting unconscionably.
You don’t care about maintaining a business relationship
Court will typically create an irreversible divide between parties. During the procession, the counselors will intentionally breakdown their clients. Litigations are intense and cause lifelong rifts.
You are a participant in a criminal, rather than civil, case
Criminal cases are meant to punish, and are the jurisdiction of the courts. Mediation is not an appropriate alternative here.
You want to attract public attention
Again, if you work for a public service agency, you might want to make the news. In these types of cases, the participants seek to make an example of the opposing participant.
You don’t care about money, time, or risk
In a criminal case, civil rights case, or human interests case there might be outside funding. Moreover, time is not as important as setting precedent and attracting public attention. Here, while risk is still great, the other factors over-ride. Furthermore, because time and money are not as much of an issue, there are many opportunities to appeal a loss.