As Pete has mentioned horses, then I will say "It's horses for courses"
Copper work hardens. It can be and should be annealed (made soft again) It usually comes already annealed, when new.
The critical thing with copper is that it needs to be well supported. Having nice neat loops in it is fine, but that doesn't stop vibration.(it will probably increase it) It just helps where there is relative movement between two parts that the copper tube is supported on.
It is not the ideal material when there is relative movement because it WILL eventually fail, in that situation.
As Pete say's Teflon is great in a heat situation. A quality Nylon type tubing would be more suitable than copper tube in the relative movement situation, IF it is protected from chaffing, excessive heat (rated?) etc.
It's a matter of assessing the application and deciding what best fits. Does it come down to price, aesthetics, reliability, performance.....