Supergirl’s Lex Luthor trial undermined the previous court cases shown in the Arrowverse. While television trials are not shown following the letter of the law, most at least attempt some semblance of credibility. Lex Luthor’s latest trial on Supergirl was obvious in the fact that it wasn’t even trying to be credible.
In the Arrowverse, both Barry and Oliver have been on trial and faced justice on Arrow and the Flash. Those trials were treated with respect and a certain gravitas about them facing the consequences of their actions. In Oliver’s trial, the prosecution presented actual evidence and testimony backing up that he was the Green Arrow, including testimony from more than just one witness. Barry was also convicted based on the multitude of evidence presented, wrongly as it turns out, for the murder of Clifford DeVoe, and spent time in the metahuman wing at Iron Heights.
On Supergirl, there were no such qualms about ensuring the show's trial reflected real life, as it was something of a formality that one took place. Writers knew there would be an outcry if Supergirl didn’t at least attempt to show him being punished for his crimes - but the focus was on ensuring Lex was rushed to freedom. He was taken to trial based on one person’s report - in National City, not a world court - and the judge let him run the trial, all of which is notably against any legitimate court proceedings.
This was the show’s first opportunity to emphasize its season 6 theme by showing someone who had abused power paying for the consequences of their crime, but this chance was squandered. The fact that Lex got a fast trial could have been a commentary on rich privilege and power, but never addressed that. Instead, it chose to act like Lex was right, making the jury believe he was victimized. While Jon Cryer manages a magnificent portrayal of Lex, it's also one that is somewhat wasted in scenarios such as these, as instead of proving how intelligent Luthor is by having him combat a legitimate court case against him and all of its nuances, an unrealistic scenario is instead crafted in order to provide him an "easy win".
With the missing Alex/Kelly scene and this trial combined, the question becomes when Supergirl will be about the protagonist again, especially given the show is coming to a close. In Lex’s case, Supergirl wasn’t the least bit interested in jurisprudence - it just wanted Lex Luthor back in the game front and center. If this is where the show intends to keep him for the rest of the season, then just go ahead and change the name of the show to Lex Luthor now.