Libadwaita is an implementation of GNOME's design, analogous to libgranite in elementary OS. This includes the visual design. GNOME only has one style, Adwaita (which means “the only one”!).
If you don't want to use GNOME's design, you don't want to use libadwaita.
> basic desktop integration on non-GNOME desktops
Libadwaita is the library you use when you're targetting GNOME.
If you want to target something other than GNOME, you don't want to use libadwaita.
Libadwaita isn't trying to be a general-purpose library for making apps that feel integrated on any platform. I don't think it's reasonable to criticise it for not being something it's not trying to be. It's like objecting that a dog doesn't meow :)
> and has it's own litany of bugs that accompany it.
Now, that is always a fair criticism :)