I'll expand on the other side of the question ... why not just add another signalling line to the interface?
That can only be asked by someone who didn't live through all the permutations of signalling lines on a genuine 25-pin RS232 interface. In addition to TXD, RXD and Gnd, there were several other pairs of signals already, RTS/CTS (Ready to Send, Clear To Send) DSR/DTR (Data Set Ready, Data Terminal Ready) and a hardware Hangup pin. And others. And no clear universal agreement between manufacturers exactly what did what function - why did you need two sets of hardware handshaking signals in the first place? And software XON/XOFF protocol on top of that) (And why did Diablo printers insist - uniquely as far as I know - on handshaking on pin 11?)
Some equipment required a full interface. Some were happy with TXD/RXD/Gnd. Some could be fooled into working by shorting pins 4 and 6 (thus looping back their own RTS to CTS). And some that should have been DCE were DTE or vice-versa and would only talk to anything else via a "null modem" cable with each pair of connections swapped.
Then to simplify all this, the IBM PC introduced a new 9-pin interface for RS232. Meaning all your existing collection of cables were obsolete and you had to start again...
All of which made life difficult even without considering that both ends may have been set to different baud rates...
This supported an entire industry built up around RS232 breakout boxes, cables and test/debugging tools.
Adding another signal, in this context, probably wasn't going to fly...