Not a fan of parallels that much.
Oda makes a point to keep One Piece free flowing, and not constrained by the past. Would rather have Luffy as the PK with Law and Kidd representing their own kind of relationship instead of just Whitebeard and Shiki.
Also
What the actual ****?
There's a difference between parallels and copy/paste. A good writer can create parallels between two or more characters while having them be unique and their own characters.
Hmm, Nope.
Law has told Luffy repeatedly that he will kill luffy even before meeting Doffy.
And Law is nothing like Whitebeard in characteristic and power.
Quake that can shake the world= Magnetic pull that can move the earth.
In fact, Kidd never once told Luffy that he will kill strawhat.
Shiki=Law
Shiki and Kid are the real parallels. Shiki and Kid are both hot-headed and violent, attacking and killing people for the smallest of reasons. They've both lost limbs that replaced with radical prosthetics and received extreme physical damage as a result of them. Their relationship with the PK parallel has been mostly friction, with Kid/Shiki showing visible and noticeable respect to the Luffy/Roger, but the latter not showing the same for the former. Both of their DFs are Paramecia that are heavily telekinetic in nature; being able to levitate objects. Shiki is called the Golden Lion because of his hair, and Kid's hair when he was a kid resembled a lion's mane greatly.
Law and Whitebeard's general personality are very much the same. They are calm, cool and collected, while Luffy and Roger are reckless and completely free-spirited, and Kid and Shiki are violent and hotheaded. Law and Whitebeard both have powers that affect the environment around them on a large scale, and does so indiscriminately and with great potency. The way Law strikes with Gamma Knife is very reminiscent of the way Whitebeard strikes with his Quake Bubbles; swinging their arms from the inside sideways to the outside and striking the enemy in the midsection.They both share similar epithets when it comes to their fruits, with Law's called the Ultimate Devil Fruit and Whitebeard's called the strongest Paramecia. Both Law and Whitebeard have family as one of their central themes as a character.
The alliance is to take out a yonkou, and that method is new because for all we know Yonkou's never existed during the golden era.
I'm just giving my opinion on similarities.
I mean Shiki wanted to team up with Rogers to take out the world government.
I don't see that characteristic in WB or Kidd
The alliance was never meant to take out a Yonko, it was meant to take out Doflamingo. Law lied about wanting to defeat Kaido and he was using the Strawhats. He told Luffy they can't kill Doflamingo because Kaido's wrath would fall on them. If Law intended to go toe to toe with Kaido, why would he be concerned about facing his wrath?
We also don't know that the Yonko didn't exist during the Golden Age.
Just because you can find traits in Shiki that don't apply to Kid or vice versa doesn't mean they can't be parallels. Being a parallel to a character doesn't mean you are both the exact same character, but that there are many and clear traits/characteristics presented in that character that can be distinctly compared.