It explains the problem: they are not a good way to express a base-20 numbering system used in the language.
(Now, you could easily augment or modify them to do that—and the creators [0] of this system initially tried that but were unsatisfied—the common way of expressing base-16 using arabic numerals plus the first six letters of the alphabet as added numerals is an example, but if you aren't using a language whose existing writing system conventionally users Arabic numerals, why would you?)
I guess I was confused about that. I didn't think that a numbering system was considered part of a language. I always thought that a numbering system was more of an ADAPTER pattern (like Hexadecimal, binary, and octal are all "addons" to the English language).
The way that a language constructs number words can have an implied base; English has an implied based 10 in most of the language (though 0-19 uses a different structure that could imply base 20 if it continued.) Most germanic and romance languages I think do something similar, though, e.g. French (FR-fr, but not some other dialects) breaks back into an implicit base-20 at 60-99.
Having numerals that map well to words reduces friction for practical arithmetic.
It used to be common to count by scores (twenties) in English, though this has mostly disappeared other than for poetical/literary usage (e.g., "Four score and seven years ago").
Dozens (twelves) were also quite common, and are still in everyday use for certain commodities (eggs, donuts, etc.).
> It used to be common to count by scores (twenties) in English, though this has mostly disappeared
Counting by scores isn't enough to be base 20. The special quantities designated by the system are still 10, 100, and 1000, an obvious sign that the numbers are conceived of in base 10. If the system pivoted around 20, 400, and 8000 (as the dozen/gross system you mention does), then you could (and should) call it a base 20 system.
Dozens even go out to another level of base 12, now that I think about it. A gross (144) is twelve dozen, so you could have something like 6 gross, 5 dozen, and 3.
The long (=great) hundred is 120, while the long thousand is 1200. It seems pretty understanding, so I wonder if anyone ever needed to use a long hundred thousand and worked out what that was supposed to be.
(Now, you could easily augment or modify them to do that—and the creators [0] of this system initially tried that but were unsatisfied—the common way of expressing base-16 using arabic numerals plus the first six letters of the alphabet as added numerals is an example, but if you aren't using a language whose existing writing system conventionally users Arabic numerals, why would you?)
[0] middle school students!