I also liked some possible links this chapter made between Doflamingo's past and his words.
His credibility with the statement ¨Kids who know peace and kids who know war have different values¨ has increased, as he himself has seen both.
The beating and lynching he got as a child and the PTSD he suffers from it would mean he knows what he was talking about when he surmised Law was traumatized from his own beating at the hands of Vergo.
I don't think having a specific reason for wanting to be the Pirate King would lessen the level of competition. if anything, having a specific reason for wanting to be PK, having a deep meaning for yourself associated with it would make you all the more determined to become the Pirate King.
That is not what Cali said.
There isn't a deeper meaning behind Law's goal of becoming the Pirate King. What Cali is saying is that Law's ambition is displaced. What he truly wants is still hidden to us, but he is aiming for Pirate King because he most likely doesn't realize it yet, or he does, but believes, wrongfully, that the wait to achieve it is through being Pirate King.
Pirate King is a completely empty title. No one who wants the title wants it for the title. The only ones who are serious contenders are those that want to be a Pirate King because of the journey to become one and, secondly, as Luffy so heartwarmingly put, because the Pirate King is the guy with the most freedom in the entire ocean. Those are the purest of intentions that no one, with the exception of Luffy, has shown. Whatever Law wants, it most likely isn't to become Pirate King, but to free himself from Doflamingo's clutches, both physically and psychologically. Once that happens, MAYBE, just maybe, his entire psyche will change, and then he'll simply want to become Pirate King in order to travel with his crew to the end of the world. But, even so, his will will probably never become as strong as Luffy.
I say that because, with the exception of Luffy, most "D" seem to fall onto alliances with other people or ideals. They usually start out as completely autonomous and brilliant, amazing punks and inspiring idiots, but throughout their live, they start to direct their lives towards something outside of themselves. Jaguar seemed like a brilliant Marine, but then his will and ambition became that of Olivia, and then Robin. Ace wanted to become Pirate King but then quickly fell with White-beard's dream of a family. Garp wanted to become a Marine, that was his dream, and wanted his children to become Marines too. I believe his will was broken by, also my theory, Dragon's defection of the Marines. And Dragon wants to rid the world of the World Government, and I also believe this dream will shift towards someone else's dream, if it was ever his from the start (I think what Dragon is doing now is carrying the dream of Luffy's mother).
And, finally, even Gol D Roger, the freest of all, somehow had his dream and entire goal changed once he reached Raftel, for reasons unknown, a clear shift from himself towards something else.
I think, amongst the "D", there are followers and there's a true King. Every generation, or maybe rarer than that, there are insanely charismatic and powerful D's, but only one king, one, say, Joy Boy. All the followers start to follow for a good and heartfull reason, but follow nonetheless. Of course, see King as something more spiritual than a mere title. Someone that grabs the attention of others and captures their allegiance. And that king, now, is Luffy.
No matter what, I think we'll see Law's dream (And Dragon's) shift towards their "follower" fate.
Blackbeard, of course, is different. If the theory I believe in is right, he descends from the D Family that betrayed the true king, and cause their loss at the end of the Void Century, and that will has become tarnished from the rest of the D's.
