One of the most popular high performance light bush planes at the moment: https://en.wikipedia.org/wiki/CubCrafters_Carbon_Cub_EX
Turbines:
The money makers: https://en.wikipedia.org/wiki/De_Havilland_Canada_DHC-3_Otte... (plus it's twin cousin)
https://en.wikipedia.org/wiki/Sherpa_Aircraft_Sherpa
So these aren't bush planes?
Edit: further, there's nothing inherent to carbon or turbines that make them unsuitable for the backcountry. Turbines are generally more reliable and have fewer moving parts. There's nothing on them that you can't fix with bailing wire that you can on a piston engine. The Wilga is overwhelmingly aluminum monocoque but if you need to fix the cowling (the main carbon part) some speed tape will do as it's not really load bearing. The cessna I took my checkride in was probably missing half it's cowling bolts :/