Why don't we use hydrophobic (icephobic) coatings over traditional anti-ice methods?
I have no doubt that a lot of experimentation has been done using coatings on GA airplanes and to the extent that a coating would work, the main problem that I see is degradation of the coating from UV and erosion.  A coating would likely have to be restored regularly and would be likely too expensive for most tightwad GA pilots.

The other thing is that clear ice that forms quickly can tend to sit in place because it's "cupped" around the leading edge and a non-stick surface may not help since the ice shape can be more or less mechanically held in place even if it's unable to actually stick to the surface.  Rime ice that tends to build up out in front of the nose of the LE would probably shed from a non-stick coating a lot better.

On a side note, your chart doesn't include "evaporative" anti-ice, which is a sub-type of heated anti-ice.  On jets this is often used with hard (non-slatted) leading edges because of the need to avoid "runback ice".  A leading edge hot enough to melt ice, but below the boiling point, will allow the water to flow back and re-freeze farther back on the non-anti-iced part of the wing.  Anti-ice systems in that case will be evaporative, that is, so hot that water immediately vapourizes when it touches (like a steam iron).  

Such anti-ice systems run at 105+ C temperatures.  A coating that could prevent adhesion of runback ice behind the LE might be quite useful and could allow those wings to run lower temperature systems (the heat plays havoc with the LE structure over the long run).

Runback ice is tolerable on slatted wings and those anti-ice systems will run a lot cooler, around 50 deg C.

On yet another tangent, I always used to wonder why some jets anti-iced horizontal tails and some didn't. Turns out you don't have to anti-ice the surface if you make it big enough.