And note that the real problem is with authentication (MACs, or digital signatures), not encryption. Public availability of those records is actually probably beneficial. It's a common misconception to think that you need to encrypt while in reality you perhaps need to encrypt, but first you absolutely must authenticate.
It took 6 months to find him, and mind you that that guy was the opposite of clever (he was talking from his bathtub, from what I remember, and he started out not even knowing the ATC language).
Also, it really makes sense to think ahead just a bit, you know. Not everything has to be triggered with an accident, and in this case we're likely talking about terrorism, since no one would do this without realising just how bad the legal consequences are.
On top of that, almost everyone in the US also has some form of collision avoidance technology now, as well (either TCAS or ADS-B).
And there's plenty of times where the only time I could hear ATC was with the squelch full open, trying to pick a faint signal out through the static. Digital modes are terrible for this.
We're talking about something like a landing clearance. It doesn't have to be completely off the chart. And yes you can inject a message like that successfully, without the ATC ever knowing.
TCAS is equally broken - doesn't have authentication codes / signatures. It's actually more vulnerable since it has higher priority than ATC.
Digital modes can encode speech more efficiently than analog modes, thus reaching further on the same link budget. For example ADS-B is "audible" as far as the curvature of the planet allows - my own antenna can hear messages from up to 200mi away.
It really is a serious problem.
See: https://en.m.wikipedia.org/wiki/Cliff_effect
https://www.selby.com.au/blog/what-is-the-digital-cliff-2
Up in the air, I can also hear AM analog voice transmissions from 200 miles away, so that's not really a good measure of performance. Both modes already do that. Benefit of having an unobstructed line of sight from several miles of altitude. :)
https://cybernews.com/news/century-old-technology-hack-broug...
It's only a matter of time before this happens in aviation, but unlike in the trains case it doesn't have to be just an availability problem (all trains stopped safely), it can be a "remote code execution" problem.