What you're missing is that positional numeral systems developed relatively late--in recorded history, which is well after number systems start to be encoded in language. Earlier numeral systems are counting systems, where zero isn't a proper number but rather a signifier for a lack of stuff.
Let's look at numbers in natural languages. In English, we start with 12 basic numbers--one through twelve--and then we start counting "three-ten", "four-ten", etc. through "nine-ten." After that, we say "two tens" (the "tens" gets corrupted to -ty in Modern English), then "two tens one", etc. Note that we're not saying "two tens zero"--that's a sign that zero is not really fundamental in our counting system (etymologically, the term "zero" in English appears to date only to around 1600, contrast that to the -ty affix that dates back to at least Proto-Germanic, although many of the numbers themselves have roots back in Proto-Indo-European).
You can also see this effect in early numeral systems. Note that Roman numerals--the most common numeral system in Europe until the Early Modern--has distinct letters for 5 (V), 50 (L), and 500 (D), which is the usual case in most of its contemporary numeral systems. The Greek numerals for, say, 666, would be χξϛ--same general principal as Roman numerals, even though it has distinct numerals for every digit rather than just ones and fives.
The actual development of a true zero and true positional numeral system appears to have only independently happened very few times. The Mesoamericans probably developed it around the same time as the Long Count calendar (exact date uncertain, but roughly contemporary with the Roman Empire). Hindu-Arabic numerals developed probably slightly later (thought to be around 400 AD or so)--and it's from this system that pretty much every modern numeral system comes. The quipu could definitely represent numbers in true positional fashion, although the dating of this is unknown to me.
Base 10 predominates in modern numeral systems primarily because of the primacy of Hindu-Arabic numerals. The derivation of number terms in natural languages shows a rather confusing panoply of numbering bases. The vigesimal and sexagesimal number systems of Mesoamerica and Mesopotamia do show residual base-5 and base-10 in their construction, and the terminology in relevant native languages tends to indicate a base 10 strata (so the number in "78" in Mayan and Nahuatl boils down to "three twenty ten eight"), which strongly suggests that these systems are chosen for accounting purposes, not for things like "counting on fingers and toes." It's also worth pointing out that the human visual system subitizes small numbers--basically, you don't need to count three objects, you just take a glance and immediately know "there are three"--and this process tends to break down around 4-6 objects. It's not hard to imagine that number systems like duodecimal or vigesimal are based on counting subitized groups.