This game has some glitchy garbage type behavior in that worst enemies are not even eligible targets for a war check if the 10 turn treaty is still intact. In other words, if the AI is fighting a war, captured a city, and just took peace for extortion, but still has precarious borders...it will sail halfway across the world to declare on you at cautious if he rolls to declare war in the 10 turns after him ending that war. He will do this even if it screws him utterly when his former rival hits him with full force while his stack is out fishing.
Even without that questionable garbage in this game, you are STILL vulnerable, because the AI could roll a really high warcheck that passes its nowarprob...and if it does that and you're a better target on the AIs targeting algorithm, it will hit you @ pleased rather than a furious AI enemy. Granted, that's somewhat unlikely, but when you play as many games as me, you see it and learn it's better to just have a good garrison city with 5-6 defenders and anti-bombardment so that if someone gets greedy/stupid you can wall them off.
Now, worst enemy does have TWO areas in which its relevant!
- Diplo: You take a hit for trading with a worst enemy. The AI flagrantly cheats to detect worst enemy trades and will give you this demerit even if it didn't know you when you made the trade. In some cases, YOU CAN BECOME A WORST ENEMY EVEN IF YOUR ONLY DEMERIT IS TRADING WITH A WORST ENEMY, a rather sore point that shows just how little our gracious game creators focused on core gameplay in favor of adding additional problems in patches.
- Trades: If an AI considers another civ worst enemy, it will not agree to new trade deals with them no matter what (exception: deals to end war). "we will never trade with you, our worst enemy!!!". Even guys who would trade tech @ annoyed like mansa will deny trades over being worst enemy, so sometimes this matters. Also useful in that resource trades between worst enemies are unlikely so that cow for horse deal the AI is trading 1:1 (another very questionable thing that happens behind the scenes in this game) isn't likely between the haters.