Mark, is there a reason most commercial and military aircraft have them but most aerobatic types don't? The possibility of tighter corners is all I see but, how much tighter do we need before the pattern starts to look like a video game.
Ken
Sorry in advance about being so long winded but this answer is complex.
Howard answered the first question I'll attempt to "answer" the second to which I preface with I don't know. My first response is regarding the loads and history. Loads on aerobatic airplanes can get quite high and design criteria reach 20 G's. This means the a flying stab would have to survive a fairly high load given the Part 23 doublet design parameter for controls. That's a pretty substantial requirement which would drive a fairly heavy attachment. This is why you see lots of these airplanes with wire braced tails. A cantilevered design can be heavy without a thick airfoil. That's a structural consideration.
In terms of performance of maneuvers is another and let's limit this to airplanes like Lasers and Extra types not MiGs and F22's as these have different criteria in the maneuver envelopes. The typical aerobatic airplane flies a number of maneuvers such as combinations of loops, roll and gyroscopic maneuvers. For loops a full flying stab would work out just fine. When we consider the gyroscopic set of maneuvers like, spins, snap rolls and Lamchevaks the full flying stab would work for some but not all.
Lets think about the main benefit of a using a full flying stab in turning flight "circular airflow". When we think of turning flight in the coeficientized realm of CA the think of the zero lift line and its relationship with the oncoming airflow. For a stabilizer elevator combination there is a finite limit as to how much the ZLL can change while there is no such limit for a full flying stab. This in turn means that turning radius is limited by the maximum lift, resulting from the increased AOA of the ZLL in a maneuver. A full flying stabilizer, on the hand, can move to wherever it needs to maintain a lower AOA. Consider the Cobra maneuver made famous by the Sukoi SU 26 where the stabilizer flying the entire time and the airplane is controllable.
For the performer the situation is different. The gyroscopic maneuvers rely on a couple of elements including stalled surfaces and propeller precession. In the spin the wing stalls and a yawing motion creates a differential AOA as result of the vertical velocity component and differential horizontal component which in turn results in an increase in drag on the slower moving wing and the faster moving wing. This feeds back causing the rotation to increase and the snip develops. Contrary to average opinion rudder input is not required to cause an airplane to spin. I demonstrate this to all of my CFI candidates taking my spin course. Depending on direction of motion and direction of the propeller rotation the precession of the propeller may aggravate or damp this tendency.
Flat spins occur when a number factors come in to play such as mass distribution, propeller precession and the amount of blanketing of the tail or AOA of the tail resulting from the rate of rotation. It's intuitive that there is a point in the rotation rate that will drive the AOA of the tail past stall. At that point the rotation increases significantly. Flat spins may or may not be recoverable. That's why we wear parachutes.
So, all of that is the foundation of knowledge needed to discuss the other gyroscopic maneuver the aerobatic show planes do, the Lamchevak and its cousins. The Lamchevak is a crazy ride and involves a complex interaction of the propeller and rates of rotation about the pitch roll and yaw axis'. The bottom line is that we drive the airplane in to a position where the precession of the propeller causes a pitch and yaw rate sufficient to stall both the vertical and horizontal stabilizers. Flying the Lamchevak you can actually feel the tail stall as the airplane absolutely take off in its rotation rate. Take notice of how the performances position the maneuver, tehy point it up 30 ish degrees and it tumblers over a ballistic ark.
So, the key to the "advanced" gyroscopic maneuvers is being able to exceed the critical AOA of the horizontal stab. Substituting a flying stab would more than likely, maybe, prevent the onset of increased rotation brought on by the surface stalling. Therefore, my conjecture is, the full flying tail isn't desirable. I could be wrong but it's a tough analysis to perform and not likely worth the level of effort to build and test as the current fleet of cool @ss airplanes are doing a good job of tumbling across the sky.