Not necessarily a conflict of interest anymore than any other business which is listed.
If they don't charge within industry standards they will lose business like any other sector, similarly if they don't win cases enough, same result. While they have a duty to their shareholders, the best way to fulfil that duty is to also give the best services to their clients and ensure repeat business.
It's not really a bad thing at all unless they are ethically challenged, which could happen to public or private companies, that's more of a management issue.
