GTK3, GTK4, and libadwaita applications do look native in COSMIC. In COSMIC Settings, navigate to Desktop > Appearance > Icons and toolkit theming. Or search "toolkit" and it will be a top result. In the context drawer that opens on the right, toggle "Apply current theme to GNOME apps". This will then allow the cosmic-settings-daemon to automatically generate CSS variables for GTK4 and libadwaita apps. If adw-gtk3 is installed, it will also apply those variables to GTK3 applications.
Qt4 and Qt5 applications are unsupported, but IgKh/CuteCosmic has a Qt6 Platform Theme that integrates with the cosmic theme system and applies that theming to Qt6 applications. Though it won't work in 24.04 because most of the KDE/Qt apps in this release are based on Qt5, and the version of Qt6 is too old.
You say that, but you probably do care at least a little.
It benefits you when an application doesn't do surprising things. Even basic things like clicking in an edit control, it's better for you if that results in the same outcome across all apps (stuff like does it select all text? does it place the caret at the end?).
I personally try to run Qt stuff only but a lot of stuff most people will run is either GTK (Firefox, thunderbird) or Qt (VLC, Krita, Libreoffice by default). COSMIC can theme GTK to match its style, and so can KDE to an extent
Qt4 and Qt5 applications are unsupported, but IgKh/CuteCosmic has a Qt6 Platform Theme that integrates with the cosmic theme system and applies that theming to Qt6 applications. Though it won't work in 24.04 because most of the KDE/Qt apps in this release are based on Qt5, and the version of Qt6 is too old.