brother, their abilities are all archived in the system, and even Judgement could access that archive to search for criminals. Their abilities are not entirely public knowledge, but it's 100% available for law-enforcers.
There are many more valuable ability yet they still report them all bro.
Exhibit A: Misaki's ability is absolutely insane, and they could have used her to control literally every powerful leaders in the world and do whatever the fuck they want, but they still report her power to the system (and now basically everyone knows what her power does), so I don't think your arguments hold much logic there.
Misaki's, and some of the other level 5s' ability are well recorded because they are the most prioritized test subjects of the Academy City. Of course the scientists of AC would make their information about their abilities out in the public because it will serve as deterrant to make sure that no one will try to invade AC recklessly.
And sure, most espers' ability are accessible to law enforcers. But a power to pseudo-copy another ability like Sha's is not something that Alleister (or any higher up from the Windowless building) would allow any normal Anti-skill or even Judgment to know about. They will either eliminate her or just outright hide that information about her ability in the databanks then offer her a position as a director.
Remember that they almost tried to kill Takitsubo because she has the potential to make AC obsolete once she reached Level 5 where she can just make everyone a Level 5 if she wants to. But the only thing that the law enforcers knew about her ability was her tracking espers' AIM, not even Mugino knew that Takitsubo can reach level 5, at best she knew that she can "hijack" someone's power if she tried really hard.
And all of this is just for the case IF the scientists did knew about Sha's ability. Your previous comment is just implying that those scientists will come into conclusion that she can copy other esper's power just from the fact that she can revive a dinosaur using fossils. Those are just hypothesis, and its useless if they cannot prove or record that she can do it. You know she can just NOT show her ability to create a whole human being with an esper power when the scientists are running tests on her. The fact that she went out of her way to secretly train in the forest to try and use two esper abilities means that she is not showing the full extent of her power, not even to the scientists.
The Parameter List would still show everything she has the potential to do up until she reached the highest level she can attain, so you were kinda right that they do have it on record. But the mere fact that AC would make the Parameter List hidden to public means that they can choose whether to hide someone's full ability or not. Heck, most teachers of AC encourage the students to work their way upto Level 5 but they don't know that once a student enter AC their full potential was already settled.