My question is a direct consequence of this question and its answers and comments.
What completely baffles me (as a non-linguist) is the claim (decision? definition?) that there can be a language on Earth (at least, the most used languages and language groups) that has no grammatical cases (at least according to my understanding of cases).
I will not talk about my personal feelings and personal conclusions - I am not an expert. But the definition of "grammatical case" taken from Wikipedia clearly states:
A grammatical case is a category of nouns and noun modifiers (determiners, adjectives, participles, and numerals) which corresponds to one or more potential grammatical functions for a nominal group in a wording.
Also, the definition of the tag "case" here on Linguistics is:
Inflectional forms that indicate the grammatical functions of nouns, pronouns and their modifiers (such as adjectives).
Case is a system of marking dependent nouns for the type of relationship they bear to their heads. Traditionally the term refers to inflectional marking, and, typically, case marks the relationship of a noun to a verb at the clause level or of a noun to a preposition, posposition or another noun at the phrase level.
So as long as a language actually sends information about "things", as long as the words are useful for transmitting a message, grammatical cases have to exist - as a minimum, in an undefined way. Before the "invention" of grammar, the cases still existed, but nobody called them so.
In my mind, any language needs at least 3 cases (or their equivalents): nominative, accusative and genitive. Dative and vocative come very close too.
So, why is it OK to claim (or: why was it defined) that a language "has no grammatical cases"? Because as long as the language can transmit information, the words of the language serve a purpose and thus have a function. And with function comes the grammatical case, unavoidably.
I can understand that the French language (or whoever) might not want to recognize the existence of its grammatical cases, or that there are some word hacks to avoid admitting the existence of cases, but the idea remains: if the words have a function inside the sentences, they have grammatical cases.
Note: it is not the main scope of this question to compare the case systems of any languages. The comparison is acceptable of course for supporting the main question.