Under $400 headphones provide quality sound that suits most users' listening needs. We listen to streaming music / video, which come with compressed sound, meaning a compromsie on quality, which becomes glaringly obvious in higher quality over $400 headphones. Why waste money for music that is already compromsied quality-wise already?

The best over-ear headphones under $400: Oppo PM-3 headphones ( most versatile closed-backed headphones with the best sound, with planar magnetic drivers that are able to reproduce more sounds accurately than the usual dynamic drivers )
The second best over-ear headphones: PSB M4U 1 (comfortable fit for many  head and ear shapes. Also have a universal single-button remote and mic on a detachable / replaceable cable. Three colors: black, red, and gray)
The third best: Blue Mo-Fi (with a unique built-in headphone amp, but are a bit heavier than above two options. Having an inbuilt amp means the headphones aren't sucking power from your phone)
The affordable, but quality headphone: Sennheiser Momentum (great bass, while still being clear, smaller ear cups, also have a iPhone-specif remote)

The best headphones:  Audeze LCD-3 Planar Magnetic Headphones (open-backed, have to listen in a quiet room)
Also worth considering:  Beyerdynamic Custom One Pro Plus headphones (physical sound adjustability using sliders on the back of the earcups, with changeable side panels on ear cups)
Also worth consdiering: JBL Synchros S500 and S700 (great for bass)