I don't think flakes can do much more declarative than "legacy" nix, rather they increase reproducibility and purity. Also their tooling doesn't offer imperative stuff by default, but I'm not sure they cover use cases previously solved imperatively. E.g. I don't think you can install user software through a flake. Sure you can create shells with software available, but that is also possible without flakes.
They cover a few things -- most notably they replace channels, which are imperative.
True. I never considered channels imperative, but rather a purity issue. But I guess this is a matter of perspective.
Unless I'm way off, you can also install user software through flakes if you add them as inputs.
I don't know about this, but that doesn't mean anything.
You can also pull a repo and 'nix run .#software' from the command-line, without entering a shell.
True, though this by default only runs the default binary, and you're probably in a shell anyways, so it doesn't save that much. Also that output is, to my knowledge, not protected by garbage collection. But my knowledge of any imperative stuff is minimal, so I don't know if that's the case there.