No matter how many times a bailiff or the judge makes an announcement for persons in a courtroom to silence or "turn off" their phones, there will inevitably be a moment when a ring, a song, an alarm or some other noise emits from such a device.  It may cause some to think the solution is not to allow them.  Some courts that I go to only allow court staff and attorneys to keep their phones.  In the federal court for the Northern District of Georgia, attorneys have to obtain a special "blue card" from the U.S. Marshals Service in order to bring their technology, including cell phones, into the federal court building.

An article in the April 2019 ABA Journal collects examples of situations where people need their phones.  I myself have see iterations of these examples.

I have seen many witnesses who want to show the court photographic evidence on their phone or text message or e-mail exchanges, Facebook or other social media posts, or video or audio recordings.  This often requires the proceedings to be halted while the witness is allowed to leave the courthouse to go retrieve the device from their vehicle and come back with it.  It is a delay that could be avoided by a more permissive device policy.  I have seen some that need to access their insurance apps in order to provide the court with proof of insurance.

Some people need to use the device for a translator using something like Google Translate.

Others may need to be able to check on sick family members or arrange for transportation of themselves or children if court is running late.

Where someone is dropped off at the courthouse and they only learn of a policy disallowing the devices on entering the courthouse, it can cause greater problems.  

The strongest reason for the bans in some places is related to safety and security.  Some point to the need to avoid photo/video documentation of witnesses testifying, which can be used to bring reprisal upon them.  Others point to the need to not allow documentation of courthouse security features.  

Others just point to the desire not to have court interrupted by sounds, noises, or buzzing.  

Some even say that the devices interfere with court reporting equipment or the courtroom sound systems.

Overall though, when it comes down to allowing litigants and witnesses to have the evidence they need to present to the court with them and not having litigants and witnesses burdened by anxiety or stress regarding those in their care or transportation, it seems like the scales of justice should tip in favor of allowing the devices.  

The reality of modern life is that device notifications are here to stay, and we do not go back in time when we step into a courtroom.