That "significant difference" is not remotely enough, because a tether is too short to provide enough rope stretch to decelerate you gently.
14+ inches of stretch is not "remotely enough" to decelerate you safely from a 4' fall???! I guess we are just going to have to agree to disagree then because I can't make it any more clear than that.
When a rock climber falls on a dynamic rope, that rope is much longer in length than a tether so you get much more potential stretch distance which allows for actual gentle deceleration.
A climber doesn't magically appear 20' above their belay. The climber starts at the belay and climbs up. So the climber will at times have a short distance between themselves and their belay, which would be very similar to a short tether.
a rock climber is also being belayed. there is rope slip Before the belayer catches the climber.
Rope slip will occur similarly around the tree, although that can't be counted on because of how unpredictable it is and I'm not including that aspect in my argument.
Additionally, the belayer is not as rigid a fixed object as a tree.
This is true, but this isn't the full story. Fixed point belaying is a common climbing technique used by many climbers when the conditions require it. A belayer flying 20 feet up in the air when being snatched by a falling lead climber can be very dangerous to the belayer and lead climber in certain conditions. So climbers will use a fixed anchor point as their belay, similar to our tether system.
If your 8 feet of tether is wrapped around a tree the max length that it can use to decelerate you is two and change feet. in reality much less because of the friction from the rope wrapped around the tree.
My example of a 4' fall on 4' of rope is based on the 4' of rope being from the girth hitch to your saddle connection and does not account for the rope wrapped around the tree. I think you will get some give in that connection, but it would be so variable that it can't be counted on and shouldn't be included in the calculation. That's why I did not include it in my example.
My rock climber has between 2.5 and 3x the distance to decelerate. And that's giving the tether way more stretch than it will have in reality, and ignoring additional stretch and slip, that will be decelerating the climber.
Again your making assumptions and blanket statements that don't always match reality. A lead climber starts at the belay and climbs up. If they were to fall in the beginning of their climb, they would be falling on a very short rope, just like our tether.
I know I'm probably coming off a bit harsh and I apologize for that. My problem is that you made a blanket statement that there's no difference in falling on a short static rope versus a short dynamic rope, which I showed to be completely false by doing the math for everyone to see. Someone can see your statement and say screw it, I'll just get a static rope since theres no difference and that could get them seriously hurt or killed. That's why I did the actual math based on the average stats of the different rope types so everyone can see that there is a significant difference between the two and make an informed decision.