There are several issues with variable props...
1. Anyone familiar with our engines or aircraft know how attached we are to the idea and practice of simplicity... meaning that we've got a bit of a philosophical objection to things like in-flight adjustable propellers.
2. To use a variable prop safely the pilot needs to know how much power the engine has at a given point and how much of that power they're applying. Normally power is measured using a manifold pressure gauge which is of course possible to do with a Jabiru, however we don't have MAP charts available - which is what pilots would need to judge safe power levels.
3. Most of the variable propellers available for Jabirus are "variable", not "constant speed". The difference there is that a constant speed prop is designed to adjust itself continually and automatically, adjusting the blade pitch to maintain a particular RPM, whereas variable propellers require operator input. In turn, because they're often not perfectly set up, that means variable props are harder on the engine. A variable prop which is being operated outside of its sweet spot is as bad or worse than a poorly matched fixed pitch prop and can do real damage to the engine.
4. Historically most variable propellers which could be fitted to a Jabiru didn't come with prop blade or crankshaft vibration / stress surveys. Needless to say, some of these have caused either propeller or engine failures. I know there are some better ones out there now but I've not personally looked at any in detail.
5. At the end of the day you've only got 80 or 120 hp (nominally) to play with. That means that on an aircraft like a Jabiru the performance gains from an in-flight adjustable propeller tend to be pretty small. Historically we've preferred 2-bladed props with relatively low blade area so that the propeller can "slip" at low speed to unload the engine a little and then work efficiently once up to speed.
Of course, if you're in an experimental category there's nothing to stop you fitting one and your local dealer will be able to give you an idea which ones tend to work best in your part of the world.