Can light GA aircraft implement fly-by-wire technology?
There are multiple factors here:

The first and main one is of course weight. Fly-By-Wire requires computers and hydraulics to actuate the surfaces in a small plane weight is critical and a FBW system may be the difference between 3 and 4 passengers in total capacity.

The next that comes to mind is certification, I'm not sure exactly how this works but I would think that FBW implementation in a current airframe would require a recertification of sorts. With that being said many GA planes flying out there like the 182, Piper Arrow and other similar things still made today are sporting designs first flown more than 30 years ago. It's a simple matter of, "if it ain't broke don't fix it".

I would think that basic service and maintenance would also become more complex and worst of all more costly. I don't know much about the cost of these systems so I wont comment father than speculation like this.

There is a safety concern in small planes (and I'm sure even bigger planes) if control feedback is not present. This Article outlines some serious concerns with the Cirrus side stick and its lack of feedback (not fly by wire but some of the ideas carry over to the FBW systems that don't have feedback).   

A Note on the 172:

The way I understand FBW leads me to think the 172 does NOT have FBW flaps. While they are electronically actuated I consider FBW (and by definition):


  ...flight control computers determine how to move the actuators at each control surface to provide the ordered response


There is no computation done in a 172's flaps to my knowledge, if you move the switch they will move. While the flaps are not directly cable driven I would consider the lack of computer to keep the 172 out of the FBW category but thats just personal opinion.

Also of note, the 172 did not always have electronic flaps - that was a later addition to the aircraft in '65.  

A Note On Cost:

Although you note that one must ignore cost in this case you really can't. A FBW system would make a GA plane even more expensive than they are. This is a very real and very limiting factor in aviation. With an unlimited budget you could develop, certify, and regularly fly a FBW small plane that was chock full of gadgets but the FAA approval process is what it is and cost is a very real limit for aircraft makers.