The very first thing we ever see: Syd running down an empty street completely covered in blood, looking terrified. It's on one of the promotional posters as well.
Even though she doesn't use it a lot, we see some idea of how powerful Syd can be. Throughout the show she manages to kill a hedgehog accidentally, knock over several hundred square feet of a forest (including multiple trees dozens of feet high), destroy a library, give someone a nosebleed, and then blow up that same person's head.
This is even acknowledged by Syd after Stan's attempt to bring out her powers involves making her angry. Seeing as she can't control them, her first response is to throw two bowling balls at him. Although they miss Stan (and very narrowly at that), they hit the wall behind him with enough force that one of the balls stays in place long after the attack.
In the same episode, after leaving Stan in the bowling alley, Syd walks home at night and we immediately see that a man—who can apparently teleport or turn into shadows—has been following her this whole time. Worse still is that Syd can apparently feel that she's being followed, yet can't do anything about it, as she doesn't have enough evidence to know who it is.
Even when you take away the whole superpowers context, Syd is still a young girl being stalked by someone who can very well harm her and her family. It gets bad enough that she freaks out at school and destroys the library as a result.
Brad reading out Syd's diary for the whole school to hear is this for anyone who has been in the closet or suffered any sort of personal trauma.
Brad's head exploding and splattering everyone with gore. Sure, he was an asshole to everyone throughout the show, but did he really deserve to die that gruesomely?
If you pause it at the right time, you can even see his eyes leaving his head.
