You can do a lot of balancing by just considering the ankles or, more generally, rotating the floor contact plane relative to the character. For side-side balance, the equivalent of "ankle balance" in the fwd/back direction is pushing down with one foot - and you can generalise this into having a target plane for the feet that. This works when the feet are at awkward angles too, and can be extended to handle the feet being on uneven terrain.
However, you can do a lot more than just balancing with the ankles/feet. If you imagine standing facing out over a cliff top, feet so near the edge you can't step, and somebody gives you a shove from behind, you use your whole body to balance/try to recover - leaning forwards at the hip and "windmilling" your arms. It's worth thinking about what these actions are actually doing, how they induce forces on your feet which are the only ones that can affect your COM - its position and velocity. Ankles/feet are good for COM position control. Upper body motion is good for COM velocity control.
There are two types of forces on the feet that are relevant - normal and tangential (the latter coming from friction). It's easy to imagine (or even do!) an experiment where there's no tangential/frictional force - e.g. standing on ice. The other extreme, where you have a single contact point (i.e. you can make use of the friction forces, but the centre of pressure is always fixed) is harder to experience - would it be possible to stand on the tip of a spike, where you have no option to balance with just "ankle control"? See the "Balance Controller (new)" video here for the answer! http://royfeatherstone.org/skippy/