my opinion is that 'challenge' and 'anything' are too abstract [so] that [I should not be able to] refer to a part of them
Has my interpolation correctly reflected what you were asking? Assuming it has:
Since much and more can be used nominally (as pronouns) and as adverbs, you have to discern the function the word is serving in a given phrase.
You can think of nominal much as a (large) portion of an unidentified or unspecified substance. A modifier is required to identify the nature of the substance, and this modifier is often expressed in the form of an of-phrase:
Is there much of that wine in your cellar?
Drinking too much of anything is a bad idea.
When the of-phrase refers to something that is not a substance, nominal much is being used figuratively:
Miso soup is not much of a challenge for western palates.
The noun in the of-phrase is being understood metaphorically as something having mass or dimension or size. But this usage is so second-nature that the metaphorical force is as faint as radiation from the Big Bang. The difficulty of the challenge is being expressed in faintly concrete terms.
Amount of substance <=> degree of difficulty
For most speakers, this would translate analogically, at a conscious level at least, to a statement of degree: "not very challenging".
Nominal more refers to a portion (of unknown size) of an unidentified substance, so that it, too, requires a modifier to identify the substance.
Do you have more of that wine in your cellar?
--Yes, I have a little more of it, only a few bottles.
--Yes, I have a good deal more of it, as the wine was on sale, so I bought a case of it.
Kimchi soup is more of a challenge to western palates.
The implication (from context) is that kimchi poses a greater challenge than other foods pose.