There's only two reasons that an external camera would be in a courtroom:

1) Someone is bringing a camera into the room to specifically intimidate someone involved with the trial.

2) The trial has national interest.

The constitution makes it difficult to prevent one person from bringing a camera into the courtroom if you let other people do so. This means that the easiest way to avoid #1 from happening is for courts to have a blanket ban on external cameras.

Many courts do have internal cameras that they use to record procedural and other matters where decisions aren't being made. But those cameras are never allowed to record the jury. There is concern that jurors will feel intimidated if they know that they're being recorded and this may unduly influence their decision making process. This is especially true following the OJ Simpson trial.

During the OJ Simpson trial the judge allowed cameras to record the jury. After the trial members of the jury stated that their decision in the case was heavily influenced by the fact that they were going to be on national TV. In particular, several of them said that they felt as though they would be ostracized in their community if they voted guilty, and the presence of the cameras in the courtroom meant that literally everyone in the country knew who they were.

Drawings are viewed as a non-intimidating alternative to cameras. Its impossible to recognize someone based solely on a courtroom drawing and the courtroom artists aren't very visible to the jury. Drawings have been a regular part of court proceedings dating back hundreds of years, and in that entire time there haven't been any complaints by jurors who changed their vote because they felt as though the courtroom drawing would cause them to be recognized.