In the name of Allah the most beneficent the most merciful
first it's important to offer our prayers in the way the prophet of Allah peace be upon him offered his prayers (it's important to follow him in every thing especially in salat ), even those things for whom our salat would be considered as correct without them are important, because we don't know if Allah accept it or not !
Narrated Abu Sulaiman and Malik bin Huwairith: We came to the Prophet
(ﷺ) and we were (a few) young men of approximately equal age and
stayed with him for twenty nights. Then he thought that we were
anxious for our families, and he asked us whom we had left behind to
look after our families, and we told him. He was kindhearted and
merciful, so he said, "Return to your families and teach them
(religious knowledge) and order them (to do good deeds) and offer your
prayers in the way you saw me offering my prayers, and when the stated
time for the prayer becomes due, then one of you should pronounce its
call (i.e. the Adhan), and the eldest of you should lead you in
prayer.
For your question i will mention some ahadith :
'Ata' reported it on the authority of Abu Huraira who said: Recitation
(of Surat al-Fatiha) in every (rak'ah) of prayer in essential. (The
recitation) that we listened to from the Messenger of Allah (ﷺ) we
made you listen to it. And that which he recited inwardly to us, we
recited it inwardly for you. And he who recites Umm al-Qur'an, it is
enough for him (to complete the prayer), and he who adds to it
(recites some other verses of the Holy Qur'an along with Surat
al-Fatiha), it is preferable for him.
from this hadith the majority of scholars said that reading fatiha only is enough for our prayers to be valid (valid doesn't mean accepted it's mean we don't have to repeat the prayer)
and reading surrah is recommendable in the two first bows ( rakaat ) ;
Al-Qadi 'Iyad quoted from some of Maliks students that reading surah after fatiha is obligatory but Imam an-Nawawi said that this statement is exaggerated (in the meaning of strange statement which is a single view which has not even a hint of majority at all) and rejected.
قال النووي : وحكى القاضي عياض رحمه الله تعالى عن بعض أصحاب مالك وجوب
السورة وهو شاذ مردود .
for the hadith of A'isha in sahih muslim about the dawn prayer it doesn't necessarily mean that he did read only fatiha .. but it mean his praying was fast .. so the hadith accept the two meanings .
and some scholars said that is from sunnah to make the two rak'aat of dawn prayer short.
