Why does a Tallit-gadol and a Tallit-katan have Tzitziyot?
Where is there a discussion that a Tallit-gadol and/or Tallit-katan must have Tzitzis or Tzitziyot?
I understand Torah says to put Tzitziyot on the corner of one's garments, but Tallit-gadol and Tallit-katan did not exist back then (or did they?).
I think your questions reverses things. We wear a tallit because we want the mitzva of tzitzit. Therefore we look for a garment which is obligated in the mitzva, i.e., has four corners (MT Hilchot Tzitzit 3:1)
The reason we want the mitzva of tzitzit is that it is an important mitzva. In the words of the Rambam (Hilchot Tzitzit 3:12)
since the Torah estimates it as so weighty that all the commandments are made dependent upon it, as it is said, "And ye shall look upon it and remember all the commandments of the Lord" (Numbers 15:39)
Our ancestors wore garments that had four corners anyway (think of poncho-like garments or capes), therefore didn’t have the need for a tallit Wikipedia explains
Though in biblical times the tzitzit were attached to such everyday garments, both the present tallit gadol and tallit katan developed subsequently to address the fact that Jews no longer wore four-cornered garments, and were in danger therefore of losing this mitzvah. [...]
In the book The Ancient Jewish Shroud At Turin by John N. Lupia [he] shows the historical development of the tallit when its design began to change during the second half of the first century CE and began to take on the forms known today beginning around 1000 CE. The long tradition of a single orthodox form of the tallit became modified in a more culturally diverse atmosphere and continued to change throughout time until it became permuted and shortened in length as the kitel, tallit katan, tallit gadol, and the more common tallit prayer shawl form know today.
