The "sovereign immunity" argument is practically never invoked, and claiming that it's a hindrance against suing any government is wrong, and arguable fearmongering. Sure, they could, and maybe we could talk about if they should even have the ability to do such a thing, but they don't really ever use it. Congress has, many times, clawed back some of the reaches of such an argument anyways.[0]
For some examples, in the many lawsuits against the NSA (from the leaks by Snowden), the government didn't get out through "sovereign immunity", but the more reasonable "illegally obtained evidence" argument.
Texas Tech used it to get out of paying Mike Leach his buyout when they fired him. Even having a law degree wasn't enough for Leach to get his day in court as the university claimed sovereign immunity and washed their hands of it.
For some examples, in the many lawsuits against the NSA (from the leaks by Snowden), the government didn't get out through "sovereign immunity", but the more reasonable "illegally obtained evidence" argument.
[0]: https://en.wikipedia.org/wiki/Sovereign_immunity_in_the_Unit...