A flutter test with zero free play links would not be representative of conditions experienced during the life of the airframe.
Definitely true! That's for flutter testing of the initial certification of the primary airplane [flight controls]. A certain maximum freeplay is required to be set up (if any is to be allowed in service), and the testing done with that. That is generally expressed for continuing airworthiness maintenance as an amount [in inches] which the trailing edge of a flight control may move freely. As I mentioned, an example of this was for the Cessna 310 elevator trim tab; 3/16" of an inch freeplay was allowed if I recall (it's been 15 years since I did that testing). When I dug into the Navajo limits, no freeplay limit was provided. My spidy senses told me that if I were to fly that plane through to 110% Vne, 1/4" of elevator trim tab travel would not be acceptable to me. This resulted in some stressful discussion with the airplane owner, with the maintenance shop in the middle. But, I asserted that the trim actuator was worn out. As Piper did not publish a limit, I applied the known Cessna limit, as the two were comparable airplanes of weight and speed. The Navajo trim actuator was disassembled, and indeed found to be well worn. An airworthy one was installed, the trim tab freeplay was negligible, and I flew the dive. I was testing wingtip survey booms, not the whole airplane.
A client took his 185 amphibian to a local airport on his way home from the weekend trip, and I was called to examine it. He reported that he had been in cruise flight (which as an amphib, is not rocket fast in a 185!), and it began to "shake like hell, and make a racket". He reported slowing it down, and eventually the shaking stopped, and he landed at the nearest airport with no delay (where we picked it up). It turned out that he had a broken elevator spar, and the outboard portion of the elevator (which appeared normal to look at) could be flexed an alarming amount - he'd had flutter. The balance weight was doing nothing to prevent flutter. The elevator was repaired, I reflew the plane, and he took it happily.
I agree that some freeplay may be acceptable in a GA airplane flight control (because the manufacturer's service manual says so), but I have yet to encounter a GA airplane where flight control freeplay or "drop" is a noticeable design feature. If there is no stated freeplay tolerance, it ends up being a pilot/local maintainer decision if the airplane is airworthy, that can be a tough one. Many maintenance manuals don't give some information a pilot or maintainer might want (Navajo!). Part 23 airplanes are required to be flutter free with the flight control system intact. I believe that part 25 airplanes must go further, and each control surface must be flutter free connected, or disconnected (can't use the flight control system to damp flutter). My certified airplane does not have any flight control counter balance weights, by design, so has a very slow Vne as a flutter margin.