"Thirteen" has primary stress on its second syllable and secondary stress on its first syllable -- that is "th2irt1een", using a notation similar to that of The Sound Pattern of English. "Thirty" has primary stress on its first syllable, but no stress on its second syllable: "th1irty". And similarly, "f2ourt1een" and "f1orty".
The stress, or lack of stress, conditions some common phonetic changes in casual pronunciation. A "t" after a vowel, a glide, or "r" and before an unstressed vowel can change to a flap, sometimes written "D", so we can get "th1irDy" and "f1orDy", but because of the stress on the following vowel, this does not affect the "t" of "th2irt1een" and "f2ourt1een".
At a even more casual level, the flap "D" can be lost, giving "th1iry" and "f1ory".
The example "s1eventy" is similar, but has extra complications. The second "e" becomes a nasal vowel "e~" under the influence of the following "n", then the "n" may be lost before "t", giving "s1eve~ty". Now, the "t" is after the vowel "e~" and before the unstressed vowel "y", so it can be flapped, giving "s1eve~Dy", then (if things get this far), the "D" is changed to a nasal flap "N" because of the preceding nasal vowel, giving "s1eve~Ny". Like oral flap "D", at a more casual level of speech, the nasal flap can be lost, giving "s1eve~y".
For other numbers, well, it just depends. It's not terribly complicated, but there is no single simple rule that will tell you what pronunciations you will find in American English.
Best Answer
I think the reason we don't say several tens of dollars is that there's no need to estimate numbers in that range.
To put it another way, if we would say several thousand people, then the emphasis is on the thousands, and we don't really care exactly how many. The instances where we do care how many dollars mitigate the usefulness of this type of a construction. The difference between say $30 dollars and $300 both of which fit under several tens of dollars is significant.
Note I can imagine saying several tens to refer to several 10 dollar bills in a context where I'm not concerned with their transaction value directly.