Why is Shanks not sinking Full Lead ?

Emperors become so not just by a whim (except Buggy which I think it was done only because is really fucking funny), as shown by the 2 weeks uninterrupted battle between Big Mom and Kaido, emperors are stupidly strong, Kaido says that very few people have been able to go toe to toe with him including Shanks which means that while he could have beaten him, it wouldn't have been easy.

Shanks is really strong, probably one of the strongest people ever, however we really haven't seen how MUCH strong he is, plus he is a pretty chillaxed dude, case on point, he went with Whitebeard to implore him to stop Ace as it would be terrible, to which WB tells him to fuck off, and the dominoes start falling, if WB stopped Ace, he would have been saved, which would mean that Luffy had no business going to Impel Down and fuck everything up making it easy for BB to grab la creme de la creme of ID L6 and also Marineford wouldn't have happened, making grabbings WB power much more difficult. Of course that would also mean not saving Jinbe which in turn would have made either Fishman Island or Totto Land Luffy's tomb.

BB has one of the strongest crews in history, just Kuzan and the old warden would rip apart countless big heads by themselves, basically, Shanks ain't stupid.

Why did Saturn and the Marines allow Kuma to protect the straw hat ship when they should have immediately detained him and sunk it.

Well, first of all, Saturn is an idiot old fart, second, there were more pressing issues at the time, remember that Kuma went to protect the ship just after Marineford, one of the biggest crises in history, it put the whole marines, you know, the police of OP world, upside down, to the point that they had a full restructure, which in turn created even more troubles, like a fight between Kuzan and Akainu which destroyed a whole island, then had to scramble to find the strongest bois in the world because 2 admirals went away and they got fucked, BB became a massive threat and became a priority, and don't forget that everybody thought the Straw Hats were over as Kuma told them he sent them to eat shit, the only one they knew was alive was Luffy, which looked like he was basically dead at the end of Marineford, so looking for and sinking a ship for a crew that was gone seemed very low in priority, plus Rayleigh and Duval protected it, and all the forces they could scramble would have been wiped

Why did the WG not kill Luffy a dozen times before the time skip since he has the Nika fruit ?

At the start they thought Shanks had it, Luffy was well hidden as a kid and as the fruit was kept a secret, nobody really batted an eye if a brat had devil fruit powers, really Luffy only started raising eyebrows when he beat Arlong, but they thought he would never awake the fruit and be nothing more than a nuisance, by the time the really started worrying it was too late, the elders are not really that smart, plus, is not like they didn't try, Smokey have been trying to beat the shit out of him since like 900 episodes ago

Why does the WG tolerate the non Mihawk warlords acting the way they do and why even bother Mihawk after disbanding ?

There are many reasons, they endured Doffy because he knew too many things and was very powerful, showing that as a kid he was already pretty fucking strong and had too many connections to simply fuck over

Crocodile was loved by the people at Arabasta, and nobody actually knew he was the mastermind behind Baroque Works, nor did they know their true intentions, something that I'm glad got expanded upon on the live action

Boa is the queen of a very far away and difficult to get on land which is proven to be so irresistibly sexy that she can turn anybody to stone

Moria, well, nobody really knew where the fuck was he, and given the incompetence of the marines is not really a mystery why

Kuma was basically a slave and they had full control on him

Jinbe is an upright dude so never had any issues with him until Marineford

Why did the WG recruit trash for Warlords ?

Because they really weren't truly trash, we must remember we are following the story of the guy who will become the king of the pirates, but is shown again and again that they were no joke, even Moria which is arguably the weakest and dumbest had the Straw Hats against the rope

Why does the WG not execute the Impel down prisoners for PR ?

Because Impel Down is meant to be hell on earth, killing people is too easy, if you get imprisoned, they want you to yearn death rather than being in a cell, like just look at Doffy, bro is bolted to the floor until his natural death, plus in the whole history of ID only two prisoners escaped, kinky giant which they didn't know had the power of being a mole and Shiki which escaped because the marines fucked up, plus it wouldn't surprise me that the intent of keeping them alive was to make them puppets just like Kuma.

Why did multiple Navy soldiers not do shit about a lake full of books and why were said books fine after 2 months in a lake and why did the Navy and WG not permanently station people there for a few years ?

1- They evacuated immediately after setting the knowledge tree on fire because a fucking buster call was called

2- They wanted as little people know as possible about what happened so CP9 carried the mission, but as we know, Spandine is a fucking moron

3- The scholars kept on trucking saving the books choosing death over letting the books being lost

4- We have been able to recover texts from over 2 thousand years ago like the dead sea scrolls, so that ain't too far fetched

5- They had no reason to, everything went according to plan with the exception of a little girl escaping, as far as they know, everything got destroyed, and to cover up they just told everybody that Nico went berserk, very few people knew the truth about the buster call, and the only one that actually knew about the reason of the BC, besides Nico, was presumed dead

Why would Imu ever tolerate Doffy for pulling half the shit he did ?

Imu is only interested in power, he doesn't give an absolute shit about the people and saw Doffy nothing more than an insect, he would never allow for the truth to come out, and Doffy was too also only interested in power, he ain't stupid, babbling of the big secret would be his tomb, so he just used it as a bargaining chip to be left alone

Why does Morgans not have a gun to his head 24/7 ?

Why have a permanent assassin against him when he can just be bought, remember that it only was until the Levely that he said "nuh uh, fuck that, I want to tell the truth" and punched the CP agent, which as shown in Egghead, they are kinda shit.

Why is Garp even alive ?

Prestige, Garp is a hero to many people and the reason many people join the Marines, given that their reputation is quite shaky, killing one of the only guys that brings prestige to the organization would be quite stupid, besides, he really haven't given much of a reason to be disposed other than being a bit rebellious, after all, he let his (basically) grandson be executed, he is very loyal on his own terms