I've tried finding an answer to your question, but ultimately it presents a false dychotomy.
I see absolutely no problem in saying that Mann is inflected for the nominative, and that dative and accusative are inflected identically. In a synchronic view the eroded inflection should be as insignificant for the analysis as it is for general English. I for one really don't know whether Tür-e goes in all cases as a remnant of the dual, or sing. Hund-e only in dative, or in how many ways Mann might be inflected in various dialects. I simply don't care because I chiefly elide those. I do know Männas as regional plural vocative.
While Mann and all other nouns except names can appear with different pronouns, they can never appear alone, except in telegram or headline style, e.g. Mann beißt Hund. This I think is a strong indicator that there's not much sense in making a distinction such as "the other words in the noun phrase have, but the noun does not [have inflection]". Because it's not unusual to describe Mann, der as the headlineform in dictionaries and similar lists.
For a silly argument one could say Mann has inflection -n in contrast to the indefinite third person pronoun man (like one cannot say that with a straight face), while the etymolog of the geminate -nn- is not well understood, but it's a purely orthographic distinction. Nevertheless, consonant stems on -n are quite usual, so the euphony is maintained.
In contrast to the general case in English, the determiners can stand alone as pronouns, like that. The only case in which the inflection is then markedly different is
nom ein Mann vs
pron ein-er, which depending on context can mean einer [der Männer] (genitivus ...) or simply quantifying einer, zwei (occasionally zwei-e when standing alone), but it's effectively ambiguous. That shouldn't detract from einer being a pronoun. It is yet in agreement with the usual agent suffix ein Schust-er, which goes to show that the nominative is in fact inflected, but strongly depending on the semantic category. Mann, for sake of the argument, is in it's own prototypical category.
There is no general rule for all cases, so one could say that the inflectional paradigm is irregular and strong. It has been simplified where case information is nevertheless present in the clitics. And one might argue that clitics are lexicalized to a degree whenever clues are missing (das / der Notebook / Laptop), or synthetic when clues like -er are present (der Computer) as far as gender is concerned. The case inflection follows regularly.
It is notable that articles developed from determiners. So it might be reasonable to analyses nouns as noun-adjuncts, complements, attributive nouns, whathaveyou to the head of the Phrase. And adverbs, if that's what that basically is, just don't inflect for case. Adjectives do. Whether that's "easier" as you put it, I don't think so, because the noun still commands the gender of the head, unlike adverbs. But there can be situations where half way into a noun phrase one suddenly has to select one of various suitable nouns (not different from any other word finding problems) so that the determiner suddenly rules the noun--more likely when the underspecified das was used.
Last but not least, compound nouns need to be considered. The fact that the adjective in groß- Mann is inflected makes it really easy, if not preferable to employ nominalization. Duden dedicates a few pages worth of writing to rules around capitalization of these constructs. I am not sure how indicative or rather arbitrary those rules are. I mean, German really get's a bad rap for compounding, if we could as well write der Große-Mann. Compare e.g. Großhändler (bulk-sales?), Klein Lisa and similar, which would impliy that in fact the bare stem is more likely to confer noun-hood, if that weren't purely conditioned by phonetics. The recommendations are summarized there (cf D 73, D 88 - 89).
tl;dr: instead of saying that the noun is not inflected, or hiding it's inflection, rather don't mention it at all. If you do mention it, it appears as a notable exception, which can be understood as irregular inflection. So the argument is self defeating. This, which might count as hiding or zero-morph'ing, is not needed because noun phrases never appear without inflection. Ultimately, it seems that stems might well count as prototypical nouns, at which point the notion of inflection becomes meaningless. Saying there was no inflection may be effectively equivalent, but not strictly the same. It's certainly still easier not to mention it.