BASIC was designed as an interactive language on the Dartmouth Timesharing System rather than batch, though. It was assumed that the user was at a terminal (probably a teletype given the era) and could interact in real time with the computer rather than punching cards to be handed to an operator and receiving output later. The line numbers were there to aid editing code as a replacement line could be entered using the same line number as an existing line. This tradition carried into the home computers of the 1980s as they generally didn't use text editors as we know them for editing BASIC code.