US Soccer should do its due diligence on the Berhalter kicking incident from 31 years ago and how Berhalter has responded to it in the years and decades since.
US Soccer should also do its due diligence regarding Gio's conduct in Qatar, and determine whether Berhalter's actions regarding Gio's playing time were appropriate or not.
While US Soccer should absolutely look into these things, it seems as though Berhalter made a big mistake 31 years ago, but has done right by it since.
It also seems as though Gio was not living up to the expectations of a national team player in terms of training intensity and other conduct. If Berhalter were full of it, we would be hearing from people that were there saying that Berhalter's account is bogus. But we haven't.
Berhalter would view Gio's playing time through the prism of his own best interests, which is to have the team be as successful as possible. The nature of the US team is generally not to go out there and out-technique the other team. The US team tends to be successful through collective effort/intensity and unity, and it seems clear that Gio's actions in training gave Berhalter enough cause to doubt Gio's fit within that setup.
I also think Berhalter didn't unfairly trash Gio to the media (assuming, of course, that Gio's training intensity wasn't up to snuff, which US Soccer should investigate). As a coach of a national team at a World Cup, his decisions are going to come under scrutiny (especially not playing one of his most talented players), and he has a right to explain them. He seemed to do so in a relatively matter of fact way - we have expectations regarding training conduct/intensity, they weren't being met, we tried to nudge the player in the right direction which only seemed to make things worse, so we had a make-or-break sit down, the player made it right with the coaches and teammates and there were no issues after that, so we used the player in matches accordingly. Berhalter could have handled it better, but this doesn't seem too bad.
All of this stems from Gio, for whatever reason, not living up to expectations in training. He seemed to think his talent and club accomplishments should exempt him from the expectations placed upon other/all team members, and when he didn't get his way, he did what most spoiled kids do - he spun a story to his parents about how the powers-that-be were being unfair to him and destroying his life, conveniently leaving out the bits about his own conduct. His parents probably did what most spoiling parents do - not seek the truth, but try to bully the powers-that-be to get what their kid wants, in this case engaging in a bunch of threats and what-about-ism, except it has all gone public and everyone can see their actions for what they are.
TL/DR - Reynas bad, Berhalter meh, US Soccer needs to genuinely investigate events and responses on all sides and act in the team's long term interests based on their findings.