Why TORVA? Does using twice orbital rate minimize prop usage for the arc? If so, the orbital mechanics there are not intuitive to me.
It is a combination of orbital mechanics and the unique arrangement of RCS thrusters on the shuttle. The shuttle's primary RCS thrusters are sized for entry control authority and are quite oversized for orbit ops, especially compared to other (much smaller) ISS visiting vehicles. RCS plume impingement becomes a major concern during shuttle-ISS prox ops.
To minimize plume impingement, the shuttle must use a digital autopilot (DAP) mode called "Low Z" between 1000 and 75 ft which inhibits the +Z (upfiring) thrusters. To perform a +Z translation in Low Z, the DAP fires +X (aft-firing) and -X (forward-firing) thrusters simultaneously. The thrusters are canted slightly such that the X components cancel out and the Z components add, providing a small braking force. A Low Z pulse must fire 11 times as long as a normal Z pulse to provide the same delta-V, so it consumes a correspondingly higher amount of propellant.
It is therefore important that the approach profile be designed to minimize the need for Low Z (+Z) braking, even if this results in more firings in -Z and the other axes. One way to accomplish this for the Rbar to Vbar transition is to increase the rotation rate above the orbital rate. Although the physicist purist in me dislikes the concept of "centrifugal force", the analogy is useful to visualize what's going on. A higher flyaround rate means a higher tangential velocity, which has the tendency to "fling" the orbiter away from the station. This increases the +X and -X delta-V needed to start and stop the flyaround, but it greatly decreases the need for Low Z +Z braking. But this only works up to a point - eventually, the flyaround rate becomes fast enough that no +Z would ever be required, but the +X, -X, and -Z requirements would increase more than enough to balance things out.
It turns out that twice orbital rate is close to optimum for the shuttle. Hence the TORVA. Serendipitously, twice orbital rate also allows a full 360 degree flyaround to be completed during a single orbital daylight pass, so the rate was standardized for both approach and the post-undocking flyaround.