Is it code to require a cable connector in a knockout box? I understand why
they should be used, esp. to help prevent the metal edges of the box from
cutting the wires, etc.

If so, do they make cable connectors that you can install as an
"afterthought," i.e., something that may come in two parts that you can
screw on over the wires (or snap on, or...) and otherwise connect to the box
without having to disconnect the wires, install the one-piece (most common)
cable connector, and then reconnect the wires?