With the weak opponent, it wasn't needed, because you'd roll over him before the WW got too bad anyway. The bad relations were achievable in a single turn, no matter how good they were at the start of the turn. To top it off, the espionage system meant that you had as many tries as you could pay for to get your spy caught. Then you could insert another rather quickly to regain the ability to investigate cities. In short, it was far too easy to exploit in every meaningful situation.
But that wasn't you original point. You said:
In Civ III, at least, it was easily exploited to provoke a target AI into declaring war on you, so you got the war you wanted without the penalties of being the one to declare. All you had to do was demand something from an AI, keep doing so until he got furious with you, then attempt an espionage mission designed to fail. Boom, war is on and you look like the poor, innocent victim. I played Civ 2, but too long ago for me to remember how well it worked.
All I'm saying is that wasn't so because you couldn't necessarily provoke a war so spies weren't as easily exploitable as you implied.