I think the idea is that you performed the exercise to create stress that you want your body to respond to by getting stronger / more aerobically fit etc in some way. So by icing, yes, you recover better, but by reducing the stress you reduce the adaptations.

Imagine you could perfectly recover with some intervention. Then weight lifting no longer works!

For examples like the ones you listed, peak performances where you’re not concerned about gainz and maybe even have to perform again soon after, it makes a lot of sense to do anything to recover quickly.