This case law only applies as long as the algorithm is not classified. As soon as any Original Classification Authority classifies the algorithm, it falls under a new category on the U.S. Munitions List and the government could then restrict its distribution.
Obviously, classifying something that has already been open source just makes it more difficult to use and numerous local copies will be retained, but it does make further distribution illegal.
This is the only mechanism I can think of by which the US government could kill Signal in its existing open-source form. It's ugly, but not unthinkable.
Wikipedia has some good info re: export of cryptography[0].
In addition, two circuits (Ninth[1] and Sixth[2]) have ruled that source code is protected by the First Amendment.
[0]: https://en.wikipedia.org/wiki/Export_of_cryptography_from_th...
[1]: https://en.wikipedia.org/wiki/Bernstein_v._United_States
[2]: https://en.wikipedia.org/wiki/Junger_v._Daley