Honesty. Luca, I could use either form in both of your sentences, depending on, as Amy says, context. There is no way to make a judgment on appropriateness without the context which the speaker finds or creates:
The court appointed me your public defender yesterday – Here, mention of a specific past time legislates for simple past.
The court has just appointed me your public defender, so let’s get to work on your case.-- Here, the adverb just and the dependent clause both link the event closely to the present.
I broke up with my girlfriend, so I couldn’t meet you as we had planned. – context shows that the breakup is thought of as a past completed action that affected only the past (a rendezvous).
I have broken up with my girlfriend, so I won’t be double-dating with you for a while. – context shows that the breakup is thought of as a condition which affects the present and future.
As you can see, only the situation can determine the ‘correctness/appropriateness/naturalness’ of use-- as is true with most language.
(PS: Glad you like the photo, Yank, but it may be short-lived.)