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 :/
Not to mention all the Basler-converted turbine DC-3s, many of which are still flying into the least hospital places on earth (like Antartica) at almost 90 years old.
They certainly do push the limit of what I'd call a bushplace. Are we going to define anything that lands on grass a bushplane? They operate in the woods, but can they actually live in the woods? Turbines need to be sent away for servicing and are very expensive. They cannot be disassembled or inspected without things like bore scopes. These are the planes that service logging camps, commercial operations, and fly back to aerodromes. They aren't the romantic planes servicing trappers or individual prospectors, the ones that sleep under a tarp most nights.
The exact same thing is true of any certified piston engine but on a shorter time table. Piston engine need to be removed and overhauled at the factory every 2000 hours and if a prop blade grazes the ground or hits a bush it needs to be removed, fully disassembled and have a die penetration test done at a minimum.
Also, a bush plane is, by definition, any logistics aircraft that doesn't need a runway which those very much fall into.
These are turbo-props. The jet bit is only a power supply to turn a propeller. It doesn't provide thrust like in a 747 or military jet. Its air intake is covered by a filter system just like any piston engine. For a given fuel consumption, the amount of air moving in/out of a turbine engine is roughly proportional to a piston engine.
Piston engines have air intakes too. A 600ish HP turbine is also moving a lot less air than you probably think.. it's not a high-bypass jet on an airliner.
Small/medium sized turbines are used all the time on helicopters, which routinely see backwoods operation.
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 :/