Novelty was long the key to patentability until cases kept coming up that were novel but considered not a substantial leap forward. Courts said it isn't really new if it could have been thought of by someone else and other very fuzzy thinking. Non-obviousness was added to try to draw a line in a theoretically non-subjective way. Section 103 requiring non-obviousness came in with the patent act of 1952. By the mechanics and details of section 102 (novelty) and section 103 they are different things requiring different showings.
The definition of obviousness in the question is incorrect, by the way. The text of section 103 is
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102 , if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
As written the definition of non-obviousness dovetails with the section above (102) on novelty. To flesh out the statue are regulation promulgated by the patent office threw the Federal Register. CFR Tile 37 XYZ.
Over the years the criteria changed and was muddled. In 1941
the SCOTUS policy was
held that an inventive act had to come into the mind of an inventor in
a "flash of genius" and not as a result of tinkering.
In 1948 we have SCOTUS saying the device utilized in that case
"may have been the product of skill, [but] it certainly was not the
product of invention"
All of this was changing and very subjective. In order to put some clear criteria in this process the 1952 Patent Law introduced the novelty requirement and the non-obvious requirement, each with some definition. A claim in a patent application can be rejected as not novel (section 102) if every element in that claim is fulfilled by a single embodiment contained in a single document that qualifies as prior art.
To reject based on being obvious (section 103) the examiner must find one or more documents that, collectively, have all of the elements in a claim. And argue that someone of ordinary skill in the art would have thought to combine them the way they are combined in the rejected claim. Furthermore, to try to limit hindsight bias there was the doctrine of requiring the examiner to find a teaching, suggestion, or motivation written in the prior art that would show that the combination, although not in the prior art was not out of the blue.
A rejection can be countered in many ways. One is to show that in making the combination, the primary prior art cited would be changed in a way that made it useless for its original purpose. If, to make a new invention starting with a bucket, the first step was make a big hole in the bottom, or turn it upside down, then the rejection would not stand.
Another is related to predictability/surprising result but that is not the core definition of non-obviousness. Or it would take undue experimentation to find the benefit of the combination. Others are a long felt need that was not satisfied previously - if it was so obvious and the result was needed, why hadn't it been done before? Commercial success and evidence of copying are also markers of non obviousness.
The TSM requirement died with the KSR case in 2007. And other cases have weakened and confused patentability questions since then but the framework is reasonably set up so it is not a matter of an examiner saying "seems obvious to me".
Could this set of criteria be reformulated without the separate concepts of novelty and obviousness? Probably - but the way the law developed got us here and there are many more important issues regarding patents for Congress to solve, like defining what "abstract" means. It has always been the case that something abstract can't be patented, but the current trend is for more and more subject matter to be considered abstract. A recent ruling was that a garage door opener was abstract.
An important issue I forgot about. Something published but not accessible - a thesis filed by author not subject matter is not usable as prior art but if has all elements of the claim then there is no novelty.
Additionally the intended use of a device is not important in a novelty analysis. Is it a very small rake or a large backscratcher? For novelty it doesn’t matter as long as the claimed structure is anticipated. In an obviousness analysis it does matter. We ask would someone combine two teachings to accomplish some result so intended use is a key to obviousness but not to novelty.