Question: The population of India is around 1.2 billion now. It was a much smaller number in the 15th century. I am not mocking, but how did so many souls come into being?
Human beings, no matter how many, are a tiny minority. There are more living entities on the tip of a pin than there are human in India. Each bacteria is a soul. More than that, every atom (irreducable quark) is a soul. There are an infinite number of souls. Sometimes the number of instances of a species fluctuates. Some species even become extinct, but the number of souls is constant at “infinite.”
Souls do not “come into being.” They eternally exist. “नित्यो नित्यानां” (nityo nityānāṁ)the upanishads say (Katha Upanishad, I believe). An infinite number of souls eternally exist. Also पूर्णं अदः पूर्णं इदं (pūrṇaṁ adaḥ pūrṇaṁ idaṁ – “from the infinitely complete comes the infinitely complete – Iśa Upanishad).
Question: Has it been written in any scriptures that there will be a lot more souls yearning to merge into Sri Krishna in Kali Yuga than in the other Yugas?
No. Quite the opposite, in Kali Yuga very few human beings seek mokṣa.
Question: Why does the Soul need to take a form?
This is an excellent question!
What is a “soul”? Bhāgavata Purāṇa 2.10.8 explains that a “soul” is the conscious entity which possesses three qualities: divinity (power of perception), substance (the body, sense organs that facilitate perception), and individuality (a specific point of view, from which one perceives).
The soul is consciousness, but consciousness cannot do anything (even perception) without it’s three intrinsic qualities of divinity, substance and individuality. So the soul inherently requires to have (1) an individual, subjective point of view, (2) to have substances and structures which facilitate its interaction with the world – a “body”, and (3) to have divine empowerment to extend its consciousness through individuality and into the substantial body.
That’s the long answer. The short answer summarizing the same thing is “the soul needs a form because the soul is an individual entity.” Individual entities require an individually distinct locus – some type of form.
If you ask why the soul must be an individual entity, the answer is “because it is consciousness.” Consciousness means awareness. When you are aware of something, you comprehend it from your point of view. So, the principle of subjectivity, and thus individuality, is inherent within the principle of consciousness.
The question can arise if the soul must have a form in the state of mokṣa, liberation. The answer is that the soul can extinguish the tangibility of its existence by remaining devoid of a form and losing itself entirely into the non-active, almost non-existent brahman, but this is a very rudimentary, elementary level of enlightenment / mokṣa. The soul can go beyond Brahman and enter the reality of Bhagavān, a reality known as Vaikuṇṭha (which is synonymous with nirvāṇa). In that condition the soul is real, tangible, and thus still has three qualities: divinity, individuality and substance. The difference is that the substance provided to the soul in material existence is an illusory substance generated by transformation of māyā-śakti, but the substance of the form provided to the soul in Vaikuṇṭha is a real substance generated by transformations of yogamāyā-śakti.