The design is inherently 1960s, at least on an aesthetic level. The lines reek of it. I like it, you like it, most of us do. But just look at design, architecture, and aerospace engineering books of the era and it's pretty obviously mid-20th century modernist (as opposed to the combination of modern and post-modern design we currently see in new buildings on the inside and out). Sure Starfleet could be going through a retro-futurist movement in the 2240s but to a 21st century audience it'll look like old technology. Some of the spy shots seem to indicate that there's a slight 60s look to the clothes and hair, but that's different because it's more believable to a 21st-century audience that those kinds of aesthetics are cyclical. Again, we're not the only audience for this movie.