Now, all I'm about to say as potential outcomes don't matter because Addy is lying, but this very much is what I think should be the PRT/Protoctorate/Cauldron's view
The Simurgh parellels are very worrying, but it barely matters compared to an unrestrained Leet power, which is what Addie implied by saying she could use other Tinkers powers without restriction. Leet's power is "make anything once", but by removing the "once" limitation it means Addy's Tinker power is "make anything".
On the bad side, this means access to every S class technology, including biotinkering, self replicating AI, dimensional manipulation, and more. (This also means she can build the most powerful EMP ever, destroying all electronics on Earth and causing a civilization-wide collapse) On the good side this means access to a universal pancrea that can cure every disease in the world, ressurection technology, anti-Enbringer weaponary, and tinker tech that can repair others tinker tech.
Even without being aware of Sting, so long as Cauldron can figure out that a large scale multi dimensional refraction can kill Endbringers/Scion they can just have Costa Brown request Addy make the technology for them and then use it. Killing Scion comes down to having a weapon that can kill him, being able to hit him through a dimensional portal, and landing the hit. Assuming Addie makes devices for the three functions and fourth piece of tinker tech that can combine the functions, she would have a functional, perfectly accurate, unavoidable, dimensional unstable instant death weapon.
Addy would never be allowed freedom again, Cauldron would just use PTV on Piggot, Armsmaster Taylor, Annette, Danny, the local Youth Guard rep, and anyone else needed to get her transfered to LA where she would never leave the PRT building because something could happen to their silver bullet. Even assuming this doesn't happen, this is a check Addy fundamentally can not cash because the PRT can justifiably ask for a technological solution to any problem in the world. Then Addy would have to make things outside of the fields she actually can tinker things in and have to admit she lied about having the power to make anything.
In conclusion, Addy has the potential to be the worst S class threat there has ever been. Endbringers can destroy cities, Addy can split the Earth in half. The PRT believes her to be an absentminded interest troll with a disregard for authority and an inability to think about the consequences of her actions. (I don't think they've gotten around to figuring out she's crazy) The PRT would come down on her harder than fanon warlord Skitter because they have to control the walking WMD.