That sounds appealing; I'm unsure that the AI could cope with it, though. It might also be difficult to ensure that the other AIs understood what had happened.
There are definitely some drawbacks, but I think some of them could be dealt with.
When your spy discovers a civ's plans, you get "proof" of what that civ is planning on doing, which is noted by the engine.
When you talk to another civ, you get a prompt like, "I have a serious matter to discuss", and then something like "The treacherous _____ are planning to attack you" with a list of all the other civs you have contact with. If you have "proof" of a civ's plans to attack, then that civ has a little icon next its name, and if you choose it, the warning is issued normally. If you choose a civ for which you
don't have proof, a pop-up says, "We don't have any proof of these allegations" and you can choose to cancel the warning, manufacture false "proof", or issue the warning anyway. Alternatively, "manufacture false war plans" might be a mission you have to give your spy, with a chance of success based on the target civ's actual likelihood of attacking the civ you want to falsely warn.
In either case, if you issue the warning without proof, depending on your relationship and some other modifiers, the civ you are warning may just take the advice, publicly denounce you as an agitator, or secretly warn the civ you've accused of what you're doing.
If you do have proof (whether legitimate or manufactured), the civ you've warned might check your allegations with their own spy, confront the civ you've warned, or launch a pre-emptive strike. If they decide they don't believe you (check their relationship with you, your reputation for being honest, their relationship with the other civ in question, their own spy's intelligence), they could just thank you for the warning and ignore it, start to be suspicious about your motives, or publicly denounce you.
And there's no reason the AI can't do all of this with another AI civ.
And if we want the human player to be susceptible to this sort of spying, the game just needs to add a "plan war against X" button that you have to press x turns before war can actually be declared. People might not like the idea that they can't declare war on a whim, but from a "realism" perspective it makes sense that your army and ministers and all of that have to have some time to prepare for war. There can always be exceptions (i.e., if the enemy has moved units close to your borders).