I can accept this, but I have to admit I got none of it while watching the show. A lot of these things sound sound like long court battles to decide, where prematurely arresting him would actually hurt the case. On a related note, if the evidence against him is just from Darcy's illegally hacked computer and the testimony of someone who was arrested for trespassing, they're going to have a tough time taking him out in court. Unless they get some underlings to flip on him, I guess.
Also, is SWORD private, government, or government funded? They seem to have authority above the FBI to take over the site. What's the difference between something being Hayward's "personal side project" and it being, y'know, a thing that the organization is just doing? I understand nothing about how that organization works from the show. That's part of what makes it hard to understand what he's being arrested for.
For starters, I'm not sure it's illegal. They weren't real kids, and he could argue that he was acting either in self defense (or that they were acting against the Sokovia Accords, maybe?). And he only shot Rambeau because she ran in front of the bullets (with super human speed). Furthermore, Darcy wasn't actually present to see any of that.
But none of that discussion actually matters. Darcy still had absolutely no right to attack Hayward when she did. At the time she rammed him, he was clearly retreating. There was absolutely no threat to herself or anyone else. She was not acting in defense of herself or others. She made a premeditated attack with a deadly weapon against someone who had removed themselves from combat. There is no place in the US where you are allowed to hunt down and murder someone just because they did something wrong to your friends a little while ago.