Why did South Indians not find even a single religion of their own?

 It is otherway.

Hinduism is a Union of Various Sects. It does not have separate identity.

1.All the sects of Hinduism with standardised rituals have its origin from South.Read an example below titled “Sri Vaishnavism”.

2.South also developed Kaumarism (Murugan Worship) and spread across various South East Asian Buddhist Nations in 15th Century.

3.18 Tamil Siddha Tradition is later adopted by 84 Nath Tradition of Adi/Machendra/Gorak lineage.

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North has lost their religion in various point in time. Shramanic religions with political support erased Hinduism. Mystics from South (Sankaracharya, Ramanuja, Madva) traveled all over the sub continent in 7–9th centuries to reestablish it and uprooted the Shramanic religions from our holy land.

Again Weaker North succumbed to invaders and bombarded by Persians and Turks -lost their religion, temples, language and culture.

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Sri Vaishnavism:

Want to taste the difference in South and North- read below:

1. You may be thinking, Vaishnavism and Sri Vaishnavism are same. It is not.
2. The complex history is reflected in the two main historical denominations of Vishnuvism.
3. South India worship Vishnu or Narayana, called Perumal as their founder, and are followers of Mayonism or Sri Vaishnavism.
4. While North regard Vasudeva-Krsna as their founder and are followers of Brahmanic Vaishnavism.
5. To make it little complicated, Sri Vaishnavism has two sects, Vadakalai (head quartered Kanchi) and Thenkalai(head quartered Nanguneri, Tirunelveli Dist).
6. Have you ever heard of Gaudiya Vaishnavism or ISKCON?

South has its own Mystics 12 Azhwars (64 Nayanmars of Shaivism, Sakthism and Murugan Worship) to follow and do not give much weightage to an Avatar Raman who is more prominant elsewhere.

1. The Sanskrit Bhagavata Purana is essentially a Sanskrit "translation" of the bhakti of the Tamil alvars.
2. Sri Vaishnavism flourished in predominantly Shaivite South India during the seventh to tenth centuries CE with the twelve Alvars. One can find idols of 12 always in Northern side of temples within first enclosure.
3. Early writings in Tamil culture Sangam literatures, Tholkappiam and epics as Manimekalai and the Cilappatikaram present Mayon / Vishnu/ Perumal. References about Krishna can be found in Manimekalai and Cilappadikaram.
4. The Alvars, whose name can be translated "sages" or "saints", were devotees of
1. Mal -
2. Tiru Mal-
3. Sri and Mal-
4. Sri and her Pati-
5. Tiru and her Pati -
6. Tirupati. and there are 108 Tirupatis.
5. Vaishnavism in the 8th century came into contact with the advaidya doctrine of Adi Shankarar.
6. Many of the early Sri Vaishnava scholars such as Nathamuni, Yamunacharya and Ramanuja, contested the Advaita Vedanta doctrines and proposed Vishnu bhakti ideas instead.
7. Sri Vaishnavism flourished in predominantly Shaivite South India during the seventh to tenth centuries CE with the twelve Alvars, (many are non brahmins, including kings and others from all communities) saints who spread the sect to the common people with their devotional hymns. The temples that the Alvars visited or founded ( ritual certifications - present day ISO) are now known as Divya Desams and there are 108 TiruPatis or Divyadesams.
1. Tirumala Tirupati is one among them and
2. Yes, worlds largest functioning hindu temple Sri Rangam also one among them and
3. Richest temple Tiru Anantha Puram included.
4. Worlds Tallest Temple Gopuram in 1956,(Sri Rangam since 1987) and Tamil Nadu State Emblem, Tiruvilliputtur Andal (who wrote Tiruppavai) temple also one of Divya Desam.
5. One can find Vishnu in any of these three, lying, sitting and standing positions in Divyadesams.
8. Their poems in praise of Vishnu in Tamil language are collectively known as Naalayira Divya Prabandham(4000 divine verses).
9. Many of the Vijayanagara Emperors and their feudatory kings of Madurai, Tanjavur, Checking, Chandragiri, Mysore who ruled South for over three centuries from 14th till 18th century are predominantly Sri Vaishnavites.