ceigered, I see that partially as an issue with direct objects and indirect objects.

English marks both indirect and direct objects in the personal pronouns. Therefore "Call me" (which might look like an accusative to your eye) is really just an indirect object. In Esperanto we use a preposition to mark an indirect object, so we say "telefonu al mi". It's not that we are "avoiding putting in an accusative", but that in Esperanto the accusative marks direct objects only, so we don't use it in cases where it's really an indirect object.

English can be confusing with the direct and indirect objects since there's so much repetition of forms. "Give it some gas" (it = indirect object; some gas = direct object) sounds just fine and can be understood pretty easily. "Give me it" is still grammatically ok but it starts to sound a little confusing, so I think most people prefer to say "Give it to me", explicitly marking "me" as the indirect object by means of a preposition.

This kind of situation repeats itself over and over; it's a similar situation with the four (or more) possible Esperanto translations for the English ending -ing. It's not really that Esperanto is so rigid and strict. It's that English is so prone to use a single grammatical ending for multiple distinct grammatical functions, and then to depend on the listener/reader to understand through context which grammatical function we are referring to.