When putting the axle inserts onto HS-compatible stuff, I usually do black (metal) inserts on one side of the object and green (plastic) inserts on the other, i.e. black on one side, green on the other. I’m wondering whether there’s any advantage to using black inserts on both sides as opposed to only one for keeping wheels, sprockets, etc. fixed on the axle.
If its not a shaft driven gear, green on both sides is recommended, because it makes it spin freely, like its on a bearing block. However if you have a shaft driven gear then its better to have 2 black inserts, which makes the connection between the gear and shaft stronger.
The forces will be distributed better with two black inserts. Looking at plastic of the gear’s square hole, the insert will be distributed across two sides now and relieve the stress on the plastic corners of the HS gear square hole from deforming.
If you’re transmitting high torque from shaft to gear, lock bars (1/8" shaft from VEX, 1/4" shaft from robosource.net ) will help keep the gear hubs from breaking or rounding out.
Or better yet, don’t put high torque through shafts and instead drive the gear with another gear 
What? The other gear would just experience the stress.
What I mean is this: Let’s say you have an arm geared 1:7 (12:84). If you were to transfer the drive from the output, that shaft has to deal with 7x the torque from the motors. If you were to instead bolt the arm directly to the gear, then the shaft has to bear none of that torque.
Oh, I see what you mean now. However, very often the low strength shafts will warp away from the other gears and cause clicking. Of course this is because of poorly supported shafts and the solution you described is the best way to power a lift.
Yes that can happen, we learned that the hard way. However, the solution we use on our claw is much sturdier, using HS 60 tooth gears with bolts through the circular inserts.