Been climbing 2-3 years exclusively 2TC and never used tether handles. I don’t use them because I didn’t assess the risk of pinching my fingers to be very high, also it’s another thing to carry and fool with. The pinch hazard is present when you fall, and I mitigate not falling.
I have had small “kick-outs” while climbing but have never fell such that i weighted the top tether. It’s always been that my foot slips off the tree a little and my hands are already on the tree and I just balance myself. I have grabbed for the tether for balance. I’m not saying it can’t happen, I’m just saying I’m not worried about it happening.
Last thing I’ll add on pinch is that there is a way to mitigate the pinch hazard by how you grab the rope. Instead of curling your fingers under and around the rope, grab the rope more with the tips of your fingers and flip the tether up. If you fall it’ll come out of your fingers fast.
Some use the handles as a way to walk the rope up the tree. It requires less slack and you basically rock forward to back to work it up. I choose to loosen my tether to easily flip it up the tree quickly. That’s just the way I like to do it.