Try one-teen, and two-teen (12) , which is consistent with fourteen, sixteen and so forth. Those two are far different, while thirteen and fifteen are only slightly changed.
The reason is historical. Up until about 300 years ago "everybody" used base 12 (duodecimal) rather than base-10 (decimal) numbers. Thus it was dozens, NOT tens in counting. The metric revolution plus Alexander Hamilton's desire to get away from the English money system (which was 12 based) ended us with a decimal counting system to go along with our decimal numerical system.
Not a real problem ... except in base 12 what we call ten and eleven are single digits - with names! And twelve, (which was the roll-over equivalent to our ten). The old names stuck.
The higher ten values are also altered, so 22 is not pronounced as twoty two.
The Etymology of Eleven
Eleven in Old English is endleofan, and related forms in the various Germanic languages point back to an original Germanic *ainlif, "eleven." *Ainlif is composed of *ain-, "one," the same as our one, and the suffix *-lif from the Germanic root *lib-, "to adhere, remain, remain left over." Thus, eleven is literally "one-left" (over, that is, past ten), and twelve is "two-left" (over past ten).