The Cirrus SR-22 (the best selling general aviation plane every year since 2003) has mechanically linked side sticks. They aren't fly by wire like the Airbus but it shows they can be linked without a complex motor system.
Are those really side sticks, though? They look much more like one half a yoke than the kind of side stick you'd see in, for example, an Airbus or an F-16.
