The problem is Iggy, that a person arrested is only a person who is reasonably suspected by the arresting officer of having committed a crime. There is no need for there to be a prima facie case that they did, and often there is not. Once they are charged, and only if they are charged, have the CPS decided that there is a case which is likely to be proved against them.
Savile was dead. There is no doubt anyway that one or more, probably more given the number of offences alleged and the clear evidence of system ( of similarities in the particulars of the allegations), would have resulted in conviction, not just a charge, against him.
The police do not name people on arrest. They meet the need for discovering other offences by asking for witnesses. In the case of the TV weatherman, not named by them, they asked for anyone who had attended the Altrincham school, and who could give information, to contact them.