Okay, i think i can provide an explanation that might help those who are still confused.
A plane on a conveyor belt/treadmill is not like a human on a conveyor belt/treadmill. The human has to move their legs to stay still, and if the speed was increased enough they wouldn’t even be able to do that, and would fly off the back.
HOWEVER the plane doesn’t have legs. It has wheels. And (providing these have frictionless bearings) it can stay still on the conveyor belt/treadmill WHILE USING NO POWER – its wheels will just spin round underneath it. If it turns its engines on, it will move forward, and its wheels will spin even faster.
The idea of the plane on a treadmill of short length just doesn’t work. It wouldn’t take off, but it would hit the front of the treadmill straight away.