Can you point to a single instance of someone or some organization being successfully prosecuted for issuing a false or fraudulent DMCA take-down request? Yes, such requests are illegal under current law, but that law is never enforced. Part of the problem (in my, possibly uniformed, opinion) is that the legal standard is too high: you have to "knowingly" issue a false DMCA request, and that is a tough standard to prove in court. There is no penalty for shotgunning take-downs every which way and seeing what sticks (and saying "oops, my bad" for the ones that don't).

Why does issuing a DMCA counter-notification not automatically trigger an investigation by the FBI?

Then there is the problem that DMCA is woefully inadequate to deal with Fair Use. Fair Use is often cited inappropriately to justify unauthorized copying that does not rightfully fall under Fair Use exceptions. However. DMCA makes no such distinction, and it is up to the entity hosting the allegedly-infringing content (i.e., the one to which the DMCA notice is sent) to determine whether the content is actually infringing. Even when an unauthorized copy of a work passes each of the four parts of Fair Use test with flying colors, the DMCA takedown requester is still not in violation of the law you cited. So there is no disincentive to issuing spurious take-down requests.