Advantages of flat/shallow woofers?

I’ve noticed that recently flat or very subtly concave/convex woofers have been trending.
I know the classical disadvantages of building them flat, what with reinforcement layers usually required to attain the required stiffness for a flattish profile.
I know that Accuton has very sophisticated manufacturing methods for their high-quality alpha-corundum drivers which surely don’t suffer from rigidity issues. But what ARE the advantages of shallow profile woofers, acoustically that is?