First, a warning : I've made only one experiment so far with this, so take it with a grain of salt : the AI aggression toward city states can be gamed to make the game easier, in at least some of the cases, and to me at least the issue I have with it is not a question of difficulty.
Context : playing Russia, deity all standard (Continent map), on a continent shared with Brasil, Scythia, 6 CS on the continent.
In my last game, I was lucky enough to first meet two close city states (both cultural, which was great !), and I was able to get a second envoy (inspiration for state workforce) in Kumasi between me and Brasil. I was planing to go to war this game, and I saw Brasil massing forces near Kumasi and my border. I diverted a few turns to mysticism to get an envoy. By that time, Toronto had been conquered by Brasil and another two CS by Scythia. I started pushing horsemen, gearing for war, and dropped the envoy in Kumasi to gain suzerainship. Brasil still attacked, I delayed their strike a bit with units in the CS border, while I kept preparing for war. I lost suzerainship at one point (didn't check if it was Scytia or Brazil actualy) and got my units expelled.
A few turns later, Kumasi fell, but I was able to regain suzerainship before (I don't know if it matters). I got an emergency out of it, which meant that I would get the CS back and also gain a free war with Brasil, without warmongering penalty, an immediate relationship boost with Scythia, 1600 gold and assorted trade route bonuses.
I am now almost done conquering Brazil, without any war weariness, and I benefited immensely from the situation. Of course, I'm not sure of the exact conditions to trigger an emergency, but I'm making the hypothesis at the moment that at least if you were planing to conquer a neighbor (which is almost mandatory in my experience), If you are lucky enough to get a doable quest and a first meet bonus, the mysticism envoy might become key to the start of your conquest. Much too early to say how repeatable this all is, but so long as you are going for early war, this looks like a relatively straightforward slingshot to penalty-less war and a great load of gold. The relationship boost (to some AIs at least) might even help protect you from other attacks while you are on a rampage.
I was playing with Magnus, but Amani might make this more reliable as you only need the first meet envoy to gain initial suzerainship, and she can act as reusable envoys later.