As far as I know, hosting apps on the Play Store (and App Store) costs money. This means that many apps have to be downloaded via other means. Sideloading facilitates this.
Piracy isn’t possible without the ability to sideload apps.
Modifying apps isn’t either. This means apps like Revanced can’t exist on iOS.
Rooting
I use Viper4Android, an amazing equalizer app that only works on rooted devices. Wavelet is a non-root alternative by the same developer, but it lacks many features and has some technical limitations.
I take care of my phone’s battery by limiting how full it charges overnight. This is only possible on a rooted device (or on Samsung, but 85% is the only option).
I want the ability to uninstall system apps. They consume resources in the background and take up unnecessary space. I imagine people with more powerful (expensive) phones don’t necessarily desire this ability.
I want to be able to customize the UI. I don’t want an alarm clock icon, a vibrate icon, two signal bars, a 4G or wifi icon and the battery icon taking up half the status bar.
Custom ROMs
With an open-source custom ROM, I can be sure that my device doesn’t have any spyware as part of the operating system.
Custom ROMs often allow more customizations and use less memory because they aren’t cluttered with useless OEM stuff.