What a shame. The topic is actually interesting.
The enemy of my enemy is my friend has strongly influenced foreign policies forever. A great example being Catholic France aiding Prodestant German states and the Islamic Ottomann empire against the very powerful Austrian empire in the 16th century.
While I disagree with being able to tell another civ that you don't like their enemy, the idea could be allowed to influence the foreign policies of AI civs in other, more subtle ways. For instance, by expanding on the idea of the 'our mutual military struggle ...' relationship modifier. If you're at war with a civ, all civs who dislike that civ would look more favourably upon you. Builders could also benefit by sending aid (gold, units) to civs involved in a war.
But it's unbalanced. Problem is that this policy gives warmonger greater advantages than it does builders. A new concept would need to be added to off set warmongering bonuses, a concept which has more baring on succesful foreign policies - that destroying an enemy isn't always a good thing.
In the 18th and 19th centuries the Netherlands was very powerful outside of Europe but weak within Europe. Its existence was ultimately down to the fact that while a number of European states would have liked to rule the territory (noticably France), no state wanted to risk seeing the rich territory fall under the control of another state since that would see a rival gain a lot of power. The Netherlands existed because the nations that might try to conquer it recognised the risk of another nation conquering it and (for the most part) upheld its sovereignty.
Incorporate the enemy of my enemy, but also incorporate the desire to maintain the status quo, the desire to prevent weak nations (regardless of wether they're friendly or not) becoming strong nations, and the desire to weaken stronger nations.