While thinking over this question in Latin community and pounding the differences in the use of composite past in French and Portuguese, I discovered that conjugation tables, discussions of Portuguese past tenses, or even Wikipedia sometimes do not even mention the composite variety of simple past (pretérito perfeito composto, aka eu tenho falado), discuss only pretérito perfeito (eu falei).
Is this tense somehow less important or very rare in modern Portuguese? Or does it have to do with the differences between the European and Brazilian Portuguese?