The Expanse series went into a fair bit of detail on the "form follows function" aspect of spaceship aesthetics, but it was a lot more near-future than Trek.

In most cases, The Expanse postulates that the most important aspect of spaceship design is cleanliness and the ability to protect the air filters and purification systems. In this case, I would assume that carpets are likely going to cause more of a headache than comfort, but who knows. Also, they'd probably want something that would not interfere with magnetic boots when the ship is in zero-g.