I did some research regarding ancient structures, and it appears that at the time of the conquest (15th century BCE, Bronze age) there were no multi-story structures in Israel (or Canaan cultures).
Toward the 10-8th centuries BCE (Iron age), there were two-story houses, but they were relatively low - not higher than 2m (7ft) (the Gemmorah rules that a 1m (some say 0.7m - 2-3ft) high structure can legally be considered a house). See canaan Home &Family. We have lots of such structures excavated, and a lot of much later generations, scattered all over Jerusalem hills. In addition, they didn't have hard ground around the houses, which also made dying hardly possible.
This leads me to the conclusion, that the wording of the verse is rather exact - the verse does only mention the fall, not death (Deuteronomy.22.8):
"כִּי תִבְנֶה בַּיִת חָדָשׁ וְעָשִׂיתָ מַעֲקֶה לְגַגֶּךָ וְלֹא־תָשִׂים דָּמִים בְּבֵיתֶךָ כִּי־יִפֹּל הַנֹּפֵל מִמֶּנּוּ׃"
"When you build a new house, you shall make a parapet for your roof, so that you do not bring bloodguilt on your house if anyone should fall from it."
I understand that in the ancient world there were additional, probably much more common dangers, such as fire, deep pits and wells, dangerous tools (see unintentional murder), dangerous animals (see payments for raging bull injuries), and more (please suggest).
As we know, this Mitzvah was chosen later to represent dangers in general (Shulchan_Arukh_Choshen_Mishpat.427.7):
אחד הגג ואחד כל דבר שיש בו סכנה וראוי שיכשול בה אדם וימות כגון שהיתה לו באר (או בור) בחצירו בין שיש בו מים בין שאין בו מים חייב לעשות חוליא גבוה י' טפחים או לעשות לה כיסוי כדי שלא יפול בה אדם וימות:
Both a roof or anything dangerous where it's probable that someone will stumble upon and fall, for example if there was a well or a hole in his yard, whether there is water in it or not, one is obligated to make an embankment ten-handbreadths high, or to cover it, lest a person falls into it and die.
Why was falling off the roof chosen as a representation of common danger?