Instead of wasting much time on discourses that are avicārita-ramaṇīya, nice (at least for some public) as long as one does not reflect on it critically, I would like to propose a very different perspective:

The Unicorn in emerging science, and its equivalent in Indian knowledge systems: the Śarabha

“If one would like to portray the debate about the existence of the unicorn as it was conducted in the seventeenth century, then the proven metaphor of the scales lends itself best to this. On one scale of the balance, the knowledge handed down in scriptures is accumulated: the testimonies of ancient, medieval and later authorities about the existence of the unicorn and the medicinal power of its horn. On the other scale one imagines the new knowledge acquired through one's own observation: the observation that what had been assumed to be unicorn horns were in fact narwhal tusks, and that the special medicinal effect could not be demonstrated. In the seventeenth century the weight of tradition still appears to be considerably greater than that of perception. The revolutionary views of Galileo and Newton have found acceptance considerably more quickly than the belief that the unicorn does not exist and never existed. ...

In the eighteenth century, the scholarly debate about the unicorn comes to a halt. It seems that science has lost all interest in the question that had been on the agenda for more than two centuries: does the unicorn exist? The question is tacitly answered in the negative. In the great eighteenth-century natural-historical standard works by Linnaeus and Buffon, no place is reserved for the unicorn among the existing animals. ...”

(W.P. Gerritsen 2003, p. 46-47, my transl. from Dutch)

“The techniques of transmission of knowledge current in India are vulnerable to the uncritical transmission of unverified and unverifiable knowledge, such as the śarabha in Āyurvedic texts: an unexisting mythological animal to the meat of which concrete remedial properties have been attributed and were transmitted over the centuries (note 41: Zimmermann 1987: 208-210). 

On the other hand, even when printing was already in use to provide quick linking of specialised talents all over the globe, it took European science several centuries before it could unmask the unicorn as a purely mythical animal based on wrong perceptions, wrong categorizations and wrong conceptualizations. (note 42: ref. to Gerritsen [2002>] 2003 pp. 46-47).”

(Jan E.M. Houben 2009, p. 13:

www.academia.edu/33028168/Houben_2009_A_Song_Against_Bad_Dreams_Magic_Superstition_or_Psychology)

See also:

Zimmermann, Francis. 1987. The Jungle and the Aroma of Meats : An Ecological Theme in Hindu Medicine. [translation of Zimmermann 1982, with updates and additions.] Berkeley: University of California Press.