The following article contains spoilers from Superman: Son of Kal-El #10, on sale now.
After being accused of murder, Jon Kent has been working hard to try and change how the people of Earth perceive him. In Superman: Son of Kal-El #10 (by Tom Taylor, Cian Tormey, Federico Blee, and Dave Sharpe), after attempting to rescue a group of people who were more afraid of him than being crushed to death by debris, Nightwing tried to cheer him up with a joke. He related to Jon's experience, citing that all heroes face a point in their lives and that it had to be some sort of rite of passage.
While meant to brighten Jon's day and make him feel less alone, Nightwing also pointed out a key aspect of being a hero: Their terrible rites of passage. Practically every major hero in the DC Universe has been accused of murder at one point or other. If it wasn't that, then they were facing some alternate evil version of themselves, or they discovered a nemesis who exists to destroy them. It points out that anyone who decides to be a superhero is almost guaranteed to be assaulted by one of these rites of passage in some way.
In Jon's case, it meant having his reputation as Superman being besmirched by misinformation. He has been publicly feuding with President Bendix for some time. When Jon caught one of the people Bendix had experimented on, the foreign dictator triggered a failsafe to kill his agent, then proceeded to frame Jon for the murder.
This is a classic trope that heroes go through at some point or other. They get framed for murder and are then forced on the run as their friends and family either try to help prove their innocence, or try to capture their friend, who they have reason to believe might have committed murder. In Jon's case, he has gotten a lighter version of this trope, having a support system that believes in him and will be there no matter what. Adding to this, he's Superman. Who would be crazy enough to try and arrest him?
Overall though, this sort of thing happens so frequently for heroes that it has become its own requirement to be a hero. It's not really hard to understand why. Superheroes are often paragons of virtue and make themselves a thorn in the sides of those who do wrong. When it becomes apparent that killing them is no easy feat, then more Machiavellian villains will result to slandering them. By taking away their public support and turning the system they tried to help against them, they in effect remove that hero's ability to operate effectively.
All of this begs the question: Why do they do it then? At this point in the age of heroes and villains there are several things that are guaranteed: Risk of bodily harm or death, mental or emotional trauma, making powerful enemies who will do anything to be rid of them, and now, being framed for murder at some point. The only people who want to be heroes are either generously brave or dangerously reckless, willing to take the chance to do their jobs.
In the long run though, even if this is a rite of passage and at the end of it their name is always cleared. Jon is also starting out better than most, as he has the trust of the people who love him, and he has done enough work to earn Earth's trust that even the words of people like Lex Luthor cannot easily destroy it with a doctored video.