A phrase for "several" multiples of ten
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.
The drug dealer had a wad of several tens.
I think "several tens of" could suggest "at least 30" and is semantically different than "tens of".
Some data that follows might suggest counter-intuitive results regarding usage in comparison with "several dozen of". In Google searches, "Several tens of dollars" is about four times as popular as "several dozens of dollars" and "several dozen dollars" combined:
- Google search "several dozens of dollars" = About 9880 results.
- Google search "several dozen dollars" = About 37,500 results
- Google search "several tens of dollars" = About 194,000 results
- Google search "tens of dollars"About 1,200,000 results (This is semantically different and only shown for comparison.)
A Google NGram search (1) shows only a few "several tens of dollars" (many of which may be a translation of a Chinese idiom) and no "several dozen dollars".
On the other hand, another Google NGram search (2) shows "several dozen" being more popular than "several tens of", as expected. However, "several tens of" is much more popular in non-fiction than it is in fiction, where "several dozen" shows an opposite trend. A quick review of the books indicates that "several tens of" is popular among technical journals; this makes sense because in that case accuracy trumps prosody.
This analysis suggests that "several tens of" could be an acceptable form, especially in technical and other non-fictional writing. Also, "several tens of dollars" seems to be more popular than "several dozens of dollars", but this is only a gross analysis.
NGram 1 = several tens of dollars,several dozen dollars,several dozens of dollars
NGram 2 = several dozen of,several tens,several dozens of,several dozen,several dozens of:eng_fiction_2012,several dozen:eng_fiction_2012,several tens of,several tens of:eng_fiction_2012
I think it's as simple as this: there's already "dozens" and "several dozen". Those are traditional, the "d" and "l" combination sounds better, it's somewhat imprecise ("baker's dozen"). And "tens" and "several tens" do get used, typically in a scientific context.