Would it be possible to reorganise these categories, which have 703 apps in total? There appears to be no distinction between them, and both contain all sorts of apps.
Reorganise 'System' and 'Utilities' categories
This is not something that Flathub maintainers can do.
I guess that Flathub simply checks the categories defined in the metainfo (or desktop) file of each app. If an app uses a wrong category, you should ask the app developer to fix it.
I’m currently revising an app I maintain (Frescobaldi, music sheets) and I’ve realized that the Utility category is not correct.
What is the difference between System and Utilities software?
This Wikipedia page might help.
See Registered Categories | Desktop Menu Specification for the spec.
We might just remove that completely from the website.