Oh wow thank you. This is genuinely excellent and immensely helpful. I think this bit:

A treadmill will only push an aircraft or whatever else along, with an acceleration that is equal to, or lower, than the rolling resistance. If you try to accelerate the plane faster, it’ll ‘slip’

As well as this video that I found where a pilot explains how under specific but unrealistic conditions you could construct a treadmill that does indeed prevent an aeroplane from taking off,

Really helped solidify my understanding of the problem. So you end up with a situation where the wheels are going to be slipping, just like the slippage created when your hand pushes a toy car on a treadmill.

Thanks!