Drivers with a physical suspension benefit from movement and time played when they’re new. After several hours of flexing, they tend to achieve something closer to their rated specs, and therefore the intended response. Similarly, stylus suspensions benefit from some early flexing as well.
Crossovers can also benefit from burn in...specifically caps, but that aspect tends to be more subtle, and there's less provable physics theory involved. Because it’s subtle, what can be heard will vary, but most of the highend speaker designers I’ve been around definitely prefer to give a new pair some burn in time.