@Nerys Myk was correct.
ENT season 4 was released only 12 years ago it's only four years older than the Kelvin Timeline films. And despite having a better production budget and a different set of writers and producers when it came time to show us a TOS era ship they gave us this:
and
.
To me that makes the visual style TOS canon. They could have done anything they wanted to do but they did that.
You're right, the Ent production staff could have used any type of set they wanted in order to represent the 23rd century Defiant. But, that they chose to replicate the 1960's design perfectly was simply a matter of preference. They didn't HAVE to perfectly emulate the 1960's, they chose too.
And yes various people have said it will all make sense including the look of the Klingons and why the tech looks the way it does. They've said that stuff.
The "it will all make sense" and the "Klingon look" parts, notwithstanding, I haven't read a single quote from the staff stating that the show will eventually explain the current look of the production. It's fine if they choose to do that, but there is no obligation to explain the technical advances made in TV and movie production technology between 1966 and 2017.
I still don't get how the look isn't "canon"?
The colors and design of the those costumes in the photo can be considered to be in-universe canon. The fabric used to make the uniforms is not canon. Lets say that a new production of Trek is presented 50 years from now, and in that time, a new synthetic fabric that is much cheaper, lighter, and stronger than cotton/wool is invented. That new synthetic fabric is then used to create the same uniforms in the picture, same design and colors.
The design of the uniforms can be considered to be in-universe "canon", but using the new synthetic fabric is not part of the canon, because locking the production into use of the only fabrics available in 2017 is not a matter of canon. Using a stronger, cheaper, lighter, new synthetic fabric, has to do with the out of universe cost of production and personal comfort of the actors. If the new fabric had been available in the 1960's or in 2017, that is what they would have used to make the uniforms.
You have to narrow your definition of the word "look".