Was ever Varna System based on Guna and/or Karm?

Question

Was the Varna System ever based on Gunas?

These few points made me to think over this question

1. Number of combinations of Gunas are infinite as it is related to humane nature and the number of Varna are only 4. How can we distribute infinite into four?

2. Human nature is not permanent, it is fluid, it keeps changing based on situation so means combination of Gunas are also changing. So how can we accommodate changing Gunas into four Varnas?

3. We don't have sufficient examples where we can see such cases.
   
   Brahmin's son is Shudra --- We dont have sufficient examples
   Brahmin's son is Vishya --- We dont have sufficient examples
   Brahmin's son is Kshatriya --- We dont have sufficient examples
   Brahmin's son is Branhmin --- We see this usually
   
   Shudra's son is Brahmin --- We dont have sufficient examples
   Shudra's son is Vaishya --- We dont have sufficient examples
   Shudra's son is Kshatriya --- We dont have sufficient examples
   Shudra's son is Shudra --- We see this usually
   
   There are more similar cases where we dont have sufficient examples of supporting the Guna based Varna system and we usually see birth based Varna in all four Varnas.

4. We saw so many examples where the King's son is becoming King and his son is becoming King and so on. If Varna is based on Guna then does it mean God/Nature is biased so only Kshatriya getting birth in King
   
   King(Kshatriya)'s son is Kshatriya --- History/Puran are full of examples
   King(Kshatriya)'s son is Brahmin --- I don't know example
   King(Kshatriya)'s son is Vaishya --- No examples
   King(Kshatriya)'s son is Shudra --- No examples
   
   How come King's son is always Kshatriya and the most talented in the whole state/region?
   This does not look Guna based.

5. I did not see any story where woman's Varna is discussed. Was Varna for Man only? Woman is also human, So she also has her own sets of Gunas so she should also belong to some Varna.

6. There is a high chance that Brahmin's son will get Brahmanical upbringing, so high chance of him becoming Brahmin, Shudra's son will not get Brahminical upbringing, so very less chance of him becoming Brahmin. Same analogy applicable for other Varna.
   
   Like:
   Kshatriya son will get upbringing of Kshatria so high change of him becoming Kshatriya
   Vaishya's son will get upbringing of Vaishya so there is a high chance of him becoming Vaishya.

By Reading Puranic stories Varna system does not look based on Guna, it's more based on birth.
Was Varna System really based on Guna ever?

Answer 1

https://vedabase.io/en/library/sb/7/11/35/ "If one shows the symptoms of being a brāhmaṇa, kṣatriya, vaiśya or śūdra, as described above, even if he has appeared in a different class, he should be accepted according to those symptoms of classification."

Clearly shows it is not necessary that varna of child is same as that of parents. Now some examples from puranas :-

1)https://www.wisdomlib.org/hinduism/book/vishnu-purana-wilson/d/doc115997.html "The son of Nediṣṭha, named Nābhāga, became a Vaiśya[10]"

2)https://www.wisdomlib.org/hinduism/book/vishnu-purana-wilson/d/doc116005.html "The son of the last was Śaunaka[7], who first established the distinctions of the four castes[8]." Vayu Purana says same thing (in footnotes).

3)https://vedabase.io/en/library/sb/5/4/13/ "In addition to these nineteen sons mentioned above, there were eighty-one younger ones, all born of Ṛṣabhadeva and Jayantī. According to the order of their father, they became well-cultured, well-behaved, very pure in their activities and expert in Vedic knowledge and the performance of Vedic rituals. Thus they all became perfectly qualified brāhmaṇas."

1 example from Aitareya Brahmana too- https://archive.org/details/in.ernet.dli.2015.104263/page/n79/mode/2up under the heading " Story of sudra rishi Kavasa" .

No, this is wrong that kshatriya's son will have high chance of kshatriya due to upbringing and similarly for other varnas .

https://www.sacred-texts.com/hin/m12/m12b015.htm "Bhrigu said, 'There is really no distinction between the different orders. The whole world at first consisted of Brahmanas. Created (equal) by Brahman, men have, in consequence of their acts, become distributed into different orders. They that became fond of indulging in desire and enjoying pleasures, possessed of the attributes of severity and wrath, endued with courage, and unmindful of the duties of piety and worship,--these Brahmanas possessing the attribute of Passion,--became Kshatriyas. Those Brahmanas again who, without attending to the duties laid down for them, became possessed of both the attributes of Goodness and Passion, and took to the professions of cattle-rearing and agriculture, became Vaisyas. Those Brahmanas again that became fond of untruth and injuring other creatures, possessed of cupidity,--engaged in all kinds of acts for a living, and fallen away from purity of behaviour, and thus wedded to the attribute of Darkness, became Sudras. Separated by these occupations, Brahmanas, falling away from their own order, became members of the other three orders. All the four orders, therefore, have always the right to the performance of all pious duties and of sacrifices."

https://vedabase.io/en/library/sb/11/17/10/ "In the beginning, in Satya-yuga, there is only one social class, called haṁsa, to which all human beings belong. In that age all people are unalloyed devotees of the Lord from birth, and thus learned scholars call this first age Kṛta-yuga, or the age in which all religious duties are perfectly fulfilled."

https://vedabase.io/en/library/sb/11/17/13/ "In Tretā-yuga the four social orders were manifested from the universal form of the Personality of Godhead. The brāhmaṇas appeared from the Lord’s face, the kṣatriyas from the Lord’s arms, the vaiśyas from the Lord’s thighs and the śūdras from the legs of that mighty form. Each social division was recognized by its particular duties and behavior."

So everyone should have been brahmin if varna of child depends on upbringing of child by parents but above verses of Srimad bhagvat purana and mahabharat clearly disagree.