Courts have traditionally been flexible in allowing courtroom media coverage but high profile estate cases are a different matter as reported in the USA Today article "Prince estate judge: No cameras at Monday hearing."
Previously, in the probate case involving his estate, the judge barred cameras, audio recordings and sketch artists. News organizations have sought to intervene in the matter to gain access, but the judge recently declined their request to be heard for the time being and allowed that he might schedule a hearing on it later.
Prince was notorious for being extremely private about his personal life so it can be surmised that he would not want the media and television cameras near legal proceedings concerning his estate. Nevertheless, given the fact Prince did not have an estate plan his estate must go through the probate process, which is open to the public by default.
If the entertainer had taken the time to prepare an estate plan that avoided probate, then he could have distributed his estimated $300 million fortune in a way that preserved his privacy.
Reference: USA Today (June 25, 2016) "Prince estate judge: No cameras at Monday hearing."