There is an inbuilt assumption in both the FARs and JAR-OPS1 that piston engined aircraft are easier to operate than turbines.

Sounds so. Does the assumption actually hold water?
On the other hand, there seems to be inbuilt assumption that turbojets and turbofans are intrinsically safer than piston engines. Piston props can fly further than 90 minutes from a diversion if they have 4 or more engines. 3 piston engine props like 2 piston engine props must stay within 90 minutes of diversion. Whereas trijets, like quadjets, can fly as far from diversion as the fuel load allows. Only twinjets are restricted to within 90 minutes of diversion.

And then there are the ETOPS privileged twinjets. Are any ETOPS privileges also given to twin piston props and turboprops? And what about three-engined piston props? And turboprops – do three-engined turboprops need ETOPS?

I would far rather have to get myself out of trouble in a King Air 200 or a Citation than in a Trislander. More levers = more opportunity to screw up 😉

Not just yourself. 17 or 18 or 19 passenger seats, plus possibly the applicable number of lap babies.

After all, it sounds that 19 passenger seats is a huge break in terms of the crew costs. From 1 crew (solo pilot) to 3 crew (2 pilots and a flight attendant). No wonder they are so popular. And IFR commercial… sounds that their basic task is to get people in and out of homes – do it reliably even if the pilot does not like the visibility and winds, do it cheap lest people are stranded where they live, and try not to crash half the population in the process…