Indeed the early jets like the Caravelle and the Tupolevs used braking parachutes. Repacking was generally the responsibility of the base engineer, as there would not normally be enough time to repack before departure; spare packed chutes would be kept in the stores at each station on the network.
Speaking as one who has packed many a parachute designed to handle just me, and found it took for ever, I wonder just how much effort was needed to handle one of these whoppers.