Well . . . first let me say that the names of the first few numbers in English are very old: in fact, they predate "English" as we know it. That's why our names for these numbers sound so similar to the words for these numbers in other languages derived from Indo-European (such as Latin, Spanish, Italian, and French). For example, "two" sounds very similar to "duo" or "dos" or "deux."
Our English number words are firmly grounded in a base-ten system, probably because humans have always had ten fingers and used them for counting. In Proto-Germanic (originally the primary source of English), the words for 11 and 12 were "ainlif" (in other words, "one left after I ran out of fingers!) and "twalif" ("two left"). No one knows for sure whether it was common to continue counting "three left," "four left," etc. If these phrases did exist, no one knows for sure why the words/ phrases beyond "twelve" eventually fell out of use.
It is possible that we retained unique number words only through twelve because of the influence of other ancient cultures that used a base-12 numerical system. The Romans, for example, used a base-twelve system, and we know that the Roman empire has had a long-lasting effect on English-- and therefore American-- language and culture.
Certainly the base-twelve system has appealed to some people as feeling more "natural," and it still appears routinely in our units of time and measurement. We still divide a year into twelve units (roughly corresponding to the cycles of the moon), and a foot into twelve equal units (inches). We still sell things by the dozen* and even occasionally by the gross (144, or twelve twelves).
But . . . the question remains, why haven't "eleven" and "twelve" been updated to words more consistent with our modern numerical system? And if such an update were to be made, what names should be chosen?
"Firsteen" and "seconteen" seem like reasonable choices to me! However, our names for "teen" numbers are also a bit inconsistent with the rest of our system, and cause problems for early learners. Fourteen, for example, sounds too much like forty . . . and why is the second digit of 14 pronounced before the "-teen"?
Some have suggested pronouncing all the teen numbers as "onety-one, onety-two," etc. When you look at 10 (which is, after all, a two-digit numeral) and compare it with the number words for 20, 30, etc., it looks as if "onety" would be a very reasonable substitute for "ten." After all, if "twenty" means two tens (20); "thirty" means three tens (30); etc., why not make "onety" mean one ten (10)?
There is a purely logical reason why this terminology wouldn't make sense. Both the suffixes "-teen" and "-ty" do in fact stand for (and are derived from) the word "ten." Therefore, if we replaced the number word "ten" with "onety," we would have automatically created a nonsense word! The "-ty" in "onety" would stand for "ten" . . . but "ten" would no longer exist, because we had just replaced it with "onety"! It's a Catch-22.
Some have suggested the prefix "tenty" (or example, "tenty-one, tenty-two," etc.) as another alternative. But this would not be a logical choice, either, because the literal meaning of "tenty" would be "ten tens," or one hundred.
Another practical difficulty is that both "onety" and "tenty" sound very similar to "twenty," which would probably lead to confusion when numbers over spoken numbers.
In my opinion, if we ever decide to substitute a standard name for the teen numbers, the most logical choice would be "ty-one, ty-two, ty-three, etc."
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*A dozen is related to both the base-12 and base-10 systems, since it stands alone as a unit measurement, but originated as a contraction of the Latin Duodecim (two + ten).
Here are some reference sites related to this topic: http://www.thefreedictionary.com/eleven
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