Good point, I forgot to mention that. The nominative is unmarked in Esperanto, but it stands in opposition to the only marked case, the accusative (in -n), and so it is treated as a case, too. While most languages don't mark the nominative, as it is a kind of default case, some actually do.
Kies etc. could indeed be called genitives, probably, although I'd probably just treat them as "possessive interrogative/relative/... pronouns". But mia etc. are adjectives, not genitive nouns. Also in German and English "my" and "mein" are treated as adjectives, not as genitive. You can see that they can receive the accusative ending.
I agree. It's obviously too fundamental to change (much too fundamental), but it really wouldn't make the language too much more difficult. Imagine:
-es/-esi for the genitive and -od/-ojd for the dative.
And a correlative case (kiele...) for method-how distinct from manner/degree-how (kiel).
Pardonu min, ĉu bonvolu diri mod, kiele atingi la stacion?
La grupo, kiod li apartenas, kunsidos morgaŭ.
Ŝi tiris la levilon kaj tiele ŝtopis la alfluantan akvon.
I know I'm replying to an old comment but; Esperanto was designed to be simple. Extra cases make it harder for some people to learn. "De" and "Al" are a lot easier to learn for people from native languages that are not already abundant with different cases.
Your native language is one with many cases, which is probably why you would prefer Esperanto to have more. (It seems more natural to you.) For me, I am glad there are only two.
That's one case, though. The accusative. Cases aren't counted by what functions they perform, but by their forms. So Esperanto has 2 cases: the one without ending, and the one with the -n at the end. By convention these are called nominative and accusative.
Mi helpas vin is not a dative case, it's accusative. You could argue that Mi donas la libron AL VI uses the dative case, but that's not a case. It's a prepositional phrase.
If you are looking at it this way and apply this logic, then I agree with you, also yes prepositions only form the cases but are not counted as ones. But you can also say English has one case even though it does not have any and there are many languages in which various cases have the same ending yet are a different one. On Wikipedia i have found ''[Esperanto has] two cases nominative/oblique and accusative/allative, [...] the adjectival form of personal pronouns behaves like a genitive case."