Why do Aveilim Say Kaddish, etc. ... ?

Q. What is the common denominator for Aveilim, when they are leading or reciting -

1. Kaddish?
2. Bensching?
3. Davening?
4. Birkot HaTorah during an Alliayh?

A. The Key common denominator may be found in the responses elicited.

In cases 1 and 2
Y'hei Sh'meih Rabbah and Y'hee Sheim Hashem m'vorach are equivalent forms of "Kiddush Hashem Borabbim".

Similarly, while leading Davening and during an Aliyah, the Aveil's Bar'chu elicits "Baruch Hashem Hamvorach L'olam Vo'ed, which is along the lines of the above

Thus the common goal is for the Avel to have the responders Bless Hashem or Sheim Hashem forever.

Q: Why does the Aveil do this?

A: It's similar to Boruch Dayan Ho'emet and Tzidduk Haddin. The Aveil publicly shows no bitterness towards Hashem. Aderabba, he goes out of his way to praise Him.

Best Regards,
RRW