I mean, we know nothing about their relationship lol, so its not good to assume we know what they trust him with and what they dont, assuming thats even the case.
Considering they trust Shanks enough to not walk into a room and fight or kill the Gorosei, its not really outside of the realm of possibility.
If it’s an assumption about their relationship, it’s one based on solid facts.
It’s a fact that Shanks‘ formative years were under Roger. He is, essentially, Shanks’ father. That should automatically set alarm bells off about any of Shanks‘ actions.
It’s also a fact that Doflamingo was not allowed to be a Celestial Dragon again.
Now, you may argue that Shanks never actually repudiated his heritage. Well, I would argue that sailing with Roger was as big a middle finger to the Celestial Dragons as you can possibly give, as a CD (which Shanks almost certainly is now). If they let Shanks back in, but not Doffy- who was pretty much a typical CD- then like I said, they are morons.
Moving on from facts to speculation
There’s the entire Yonko thing. I cannot think of a single advantage the World Gov gain by having a Holy Knight masquerade as a pirate and rise to that level. It’s not like the Yonko have regular conferences to decide the future of piracy. Then a double agent makes sense. But Shanks is just one of four emperors, all opposed to each other, who are the big wigs of countless pirates, all enemies of each other. There’s nothing that Yonko Shanks can accomplish that benefits the World Gov that an Admiral Shanks couldn’t. If they wanted a sleeper agent, they should have told him to go join up with Whitebeard or Kaido so he could influence them. Or kill them.
That actually benefits them.
And if the argument is, maybe they aren’t
letting Shanks do it, he’s just so strong or so willful they can’t stop him- then wtf are they keeping him as a HK? There is a super strong, uncontrollable man who, again, was raised by their greatest enemy, and they still have him in this position? That is, like I said, idiotic.
As to trusting him not to meet the Gorosei- absolutely does not require him to work for them. Actually makes Shanks a weaker character (Not in the power-levelling sense.) Shanks being able to do that because Shanks is fundamentally known worldwide as a man worthy of respect and trust is far better than Shanks being their subordinate. He‘s simply not the kind of person who would assassinate people under the guise of a meeting.