Torque actually does matter. Torque is equal to the moment of inertia times the angular acceleration, and angular acceleration will affect how long your spin up time is (since spin up time is essentially how long you need to get to a target angular velocity)
I indeed think that team can try and tune the flywheel for best performance possible.
The most important factor of a flywheel would be its spin up time and its recovery time, and they are mostly affected by the torque and moment of inertia (MOI). Reducing spin up and recovery time means that you are able to shoot more frequently.
The torque of a flywheel is dependent on its motor count, gearing and efficiency. Since torque is equal to moment of inertia times the angular acceleration, increasing torque can increase the flywheel’s angular acceleration. This means that the flywheel would be able to accelerate more and reduce the spin up and recovery time.
The MOI of a flywheel is dependent on its mass, size and how the mass is distributed. The act of shooting a disk is essentially transferring energy from the flywheel to the disk. Since kinetic energy is equally to 0.5 * MOI * angular velocity^2, increasing the MOI of the flywheel means that you would lose less angular velocity after the shot, and therefore can get back to speed faster.
However, increasing the MOI does have its drawbacks. since as said earlier, torque is also related to MOI, increasing MOI would lower your angular acceleration. It is possible that at a point, the MOI is so large that even though less velocity is lost, the acceleration is so low that it still takes longer to recovery. Therefore, the relationship between torque, angular acceleration, and MOI should certainly be tested or calculated by teams to ensure optimal performance.
Another factor that can affect spin up and recovery time is the control loop (programming) you use. Since you are trying to control and maintain the velocity of the flywheel, having an effective, well tuned control loop can reduce the time needed for the flywheel to get up to speed and stabilize. Some of the most common control loops for flywheels I see in vex are PID (sometimes with feedforward and derivative filtering, take back half, and bang bang control. You can even try out things like state space control if you feel more advanced.
Overall, there are a lot of factors that go into making an effective flywheel. I would strongly suggest each team to test / analyze these factors in order to have the best flywheel possible.