I think this is because it is pretty boring to film a computer in action, because it does noting - it doesn't move for example. So beeping sounds were added for every action a computer would do: opening or closing windows, transferring files to a disk, calculating,...

These sounds were added at a time computers were not that common in every household and to emphazise that the computer is doing something. In recent movies, computers are more silent.

Another thing film makers did to show interaction with a computer is the constant usage of the keyboard. Every thing is done with the keyboard. Open a window: type 5 sceonds on the keyboard. Transferring a file onto a disk: type the whole bible on the keyboard. This was done because it would be pretty boring to show someone use the mouse or drag-and-drop files.

It its somehow compareable to the movie trope of constantly reloading a gun. You can see this often in older movies: the protagonist is going inside a building and he is reloading his gun. Then he stops a the corner of a hallway and is reloading the gun again - despite no shot has been fired. This was also done to show the audience that a gun will be involved.