Reasons I've jailbroken in the past:
- A firewall app, which prevents apps from talking to places I don't want them to, and also acts as a pseudo-adblocker anywhere, not just Safari
- A music player mini-mode floating window
- An actual dark mode extension, or if you don't want to buy that, a dark keyboard extension
- An extension that adds a quick-switch area in the notifications pull-down window, so I can switch things like wifi, airplane mode, even the LED light on and off without having to boot into the Settings app
- The obligatory customizing reason; I've hidden the dock on my tiny iPhone 4, hidden icon name labels, changed a few of the app icons, and probably other things I can't remember that I'm too used to
- An extension that "fullscreens" folders, instead of having a cramped app-shaped "folder"
- f.lux is only available on jailbroken devices