Does Islam produce an uneducated society?

The Quran and Hadith both hold men of knowledge superior to the ignorant. (39:9) The books of hadith have a whole lengthy chapter devoted to the importance of knowledge, and the rewards of teaching and learning.

For instance, there is a tradition that one who treads a path in search of knowledge has his way paved to paradise by God as a reward for this noble deed (Bukhari, Muslim)

In a tradition recorded by Tirmidhi, angels in heaven, fish in the water and ants in their dwellings pray for the well-being of a seeker of knowledge.

In another hadith the Prophet of Islam observed, those who learn virtues and teach it to others are the best among humankind (Al-Bayhaqi).

Not more than 150 people all over Arabia knew how to read and write. They made the maximum use of their ability to memorise, preserving their entire literary heritage in their memory. There is no trace of any systematic or organised activity of learning or teaching in the society. But soon after the revelation of the Quran, the trend of receiving education set in, and everyone who accepted Islam learnt the Quran from the Prophet, and after learning it himself taught to other converts. In this way the homes of the early Muslims—Abu Bakr Siddiq, Al-Arqam bin Al-Arqam, Fatimah bint Khattab—turned into centres of learning. Moreover, from the very outset, the Prophet appointed scribes who were assigned to write down the Quranic portions as soon as they were revealed. This motivated others as well to learn writing so that they might make their own copies of the holy textbook. It is to be noted that even under life-threatening circumstances, when the Prophet had had the first and second pledge at Al-Aqabah, three years before the migration, he appointed twelve people who were most learned amongst them as teachers of the Quran. These teachers were so sincere and enthusiastic that within a short period of three years they spread the knowledge of the Quran to almost each and every home of the tribes of Al-Aws and Al-Khazraj. Hence when the Prophet arrived at Madinah in the 13th year of his Prophethood, he found all the young and old people of these tribes well versed in the teachings of the Quran.