> instead of shutting down Parler directly the approach would be to send a complain to a relevant federal authority (not sure which one that would be, maybe the FBI? please correct me) and let them do their investigation.

It has been suggested by many people that in fact the causality goes the other way. The reason for the near-simultaneous action against Parler from Twilio, Google, Apple and Amazon seems likely to have been a strong suggestion from Federal law enforcement about an imminent threat.

There's no evidence for that per se, but certainly the threat seems imminent.