The general requirement of recitation in prayer and the specification of al-Fatihah are distinct legal questions. Hanafi jurists distinguish proof establishing the underlying act of recitation from further proof requiring a particular recitation.
The question is not whether al-Fatihah is good to recite, but what level of evidence establishes its specific requirement. In Hanafi jurisprudence its recitation is categorized as wajib, whereas the foundational integrals of prayer are classified separately.
The effect of an omitted component on the validity or rectification of prayer depends on further rules. The present example concerns the evidentiary distinction between fard and wajib.