Accusative and Dative

Meanwhile, there's something that has been bothering me for some time:

Why doesn't Estonian have Accusative and Dative cases? It has more cases than any language really needs, but not an Accusative or Dative case?

Russian has Accusative and Dative cases. German has Accusative and Dative cases. Finish has an Accusative case and a Partative case for the direct object (I'm not sure what it does for it's indirect objects)...

Since all of the major language that would influence Estonian have at least an Accusative case, why doesn't Estonian?

Surely, like Finish, it must have had an Accusative/Partitive thing happening for direct objects. What happened to the Accusative? Why did it decide that the object of a sentence could be in anyone of the three base cases? How did the Genitive case get to be the main go-to case for total objects?

Coming from a language that relies heavily on the subject-verb-object relationship, it seems odd to me. Like someone created a person without any feet, and then tried to come up with a variety of foot-substitutes. Functional? Well, yes. Practical? Not so much.

Then again, a lot of Estonian seems like that.