Trolls should be banned because they disrupt serious discussion. Identifying trolls is often difficult, however. I like to think in terms of "troll score": the higher the troll score, the more likely it is that a person is a troll. Examples of things that affect troll score:
...
- Requires more moderation than is typical: moderate increase
- Using vulgarity, insults, or memes excessively: mild increase
- Criticizing moderation: moderate increase
- Complaining about anything: small increase
- Uses ad hominem attacks with unusual frequency: moderate increase
- Lying: moderate increase
- Posting topics that will obviously evoke emotional responses: slight increase
- Posting replies that are themselves on-topic but which will obviously tend to bring the discussion off-topic: moderate increase
...

None of these things alone warrant a warning, but when they occur habitually or when someone does many of them, they indicate that the poster is a troll.

Warn people who are doing many trollish things. Tell me if that doesn't help.