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First, sorry if I'm not using the correct terminology here.

By "word-based", I mean typical Indo-European languages (plus Uralic) where there are only tens of characters (e.g. "A to Z" (Latin) or "А to Я" (Cyrillic)), and a character alone has no meaning, unless it happens to be a complete word ("I" in English is both a single letter and the nominative first person singular pronoun).

By "character-based", I mean languages like Chinese and Japanese, where any single character has its specific meaning.

I have wondered that, how would a word-based language to exist with absolute zero word inflection. A word inflection is like the plural form of a noun, or noun declension by case (Latin, German, Icelandic, Finnish etc.), or verb conjugation (Romance languages, East Slavic), or affix-based adjective and adverb distinction. Periphrastic affection doesn't count (e.g. Perfect "tenses" in English, which is constructed with auxiliary verb "have").

In Chinese, there's absolutely zero word inflection. Nouns do not have plurals or declension, verbs do not vary by tense or person, and they don't even have participles. This, IMO, relies heavily on the fact that Chinese is a character-based language.

English, AFAICT, is the language with the least word inflection features among all Indo-European languages. Nouns have at most 2 forms, and verbs have at most 5 forms (except "be"). Adjective only has one inflection (-ly turns into adverb).

How would such a language be, if word inflection fades away utterly?

There is no such categorization of languages as "word-based" vs. "character-based".

Not all Chinese speakers are literate. Standard Chinese has certainly been affected by the character-based writing system, and this affects how people speak, but linguists generally don't consider the paucity of inflection in Chinese to rely heavily on the existence of characters.

Vietnamese is currently written with an alphabet, but it doesn't seem to have any more inflection than Chinese.

Hawaiian seems to have no verb inflection, even though it is not written in characters, and I can't find much sign of any other word category being inflected either.

Having some amount of inflection seems to be pretty common, and the amount/types of inflection that we see in a language seems to be influenced somewhat by the region. The type of writing system that a language has is strongly influenced by its region: writing is only thought to have originated independently a small number of times. East Asia is a linguistic area where low levels of inflection are common, and Han-character-based writing systems have historically been used. This is not enough data to make a conclusion about whether there is a causal relationship in either direction between character-based writing systems and lack of inflection. There is no obvious linguistic obstacle to a language having no inflection and no character-based writing system.

The problem is, things like "word-based" vs "character-based" as you put it (the standard words are alphabetic vs logographic) apply to writing systems, not languages. Languages, both historically and even nowadays, are spoken more often than they're written—you can find people who speak English, or Chinese, or almost any language, perfectly well, even though they can't read or write.

You're right that inflection and logographies don't fit together well. But languages can be (and often are) written in systems that aren't at all suited for them: look at the lengths English goes to, to represent 40-some phonemes with 26 letters, and the chaos that results. Japanese used to be written entirely with Chinese characters, which weren't a good fit for all its verb inflection—modern Japanese has repurposed a small subset of these characters into phonetic "kana", in an attempt to fix that problem.

In addition, the line between derivation (making new words) and inflection (changing the same word) isn't always a clear one. English has, at most, eight inflections: two on nouns, four on verbs, two on adjectives. Things like -ly are almost always considered derivation, not inflection. But what about -est? Is "largest" a new adjective, or just a form of "large"? Is 's an inflection or an enclitic? How do you even decide what counts as the same word and what doesn't?

So unfortunately, the best answer I can give is: this question can't be answered in its current state. It is probably true that Chinese kept a logography because it doesn't have inflection, while the Egyptian logography slowly turned into the Latin alphabet (via Semitic and Phoenician and Greek) because all those languages have more inflection. But this is a case of the language affecting the writing system, not the other way around.