It sure is easier to develop with a game engine. Unity engine is pretty good for that, with its visual editor, good asset import pipeline a tons of stuff on Asset Store that would help to boost your development. There are other game engines tyou could use for live wallpapers, but it'd be a much more tedious task.
The negative side of using Unity is that ti might be somewhat heavy - it's expected to have an minimal APK of around 9 MB in size This doesn't really matters if you have a resource-heavy live wallpaper, though.
I've recently released uLiveWallpaper - a Unity asset that makes it possible to create live wallpapers for Android using Unity 5. It is well-tested and reliable, creates projects for Android Studio, complete with placeholder code to get you started.
Unity is probably not the best option if you want to make something really simple, but definitely the best option if you aim for high visual quality.
Check out uLiveWallpaper forum thread here:
http://forum.unity3d.com/threads/ulivewallpaper-develop-android-live-wallpapers-with-unity-5.375255/
Or just search up for "uLiveWallpaper".