A couple of examples of use cases: 

A call for this came from the arabic layout requirements task force at the W3C yesterday, since Iranians want more control over defining list counters.

Working on vertical text recently i have also seen a need to allow users to define counters such as circled-decimal (http://w3c.github.io/predefined-counter-styles/#circled-decimal) so that counters in vertical text stand upright. 

Firefox already has good support for the counter-styles spec.

I put up some basic tests and results. See https://www.w3.org/International/tests/repo/results/counter-styles.en.html  (click on the large text in the left-most column to run the tests)

Another use case is traditional in Russian typography list bullet. Not a dot •, but — medium dash. It’s currently not possible to use it easily, apart from pseudo-element with content way, which is quite a workaround.

So it should look like this:

— One
— Two
— Three

@counter-style would make it possible.

> Another use case is traditional in Russian typography list bullet. Not a dot •, but — medium dash. It’s currently not possible to use it easily, apart from pseudo-element with content way, which is quite a workaround.

That doesn't necessarily need @counter-style, though. list-style-type accepts string, though that is only supported in Gecko at the moment as well.

Okay filed another issue for that on Issue 687946 and https://bugs.webkit.org/show_bug.cgi?id=167729

In traditional French typography list are also introduced by a dash (tiret) rather than a bullet (puce). 

It also affects Japanese, Chinese and Korean numbering, which should use "、" or "," instead of "." after each counter. See https://github.com/w3c/jlreq/issues/12 as discussed in w3c Japanese layout requirements task force.

Additional requirements. Current implementations support myanmar and shan digit based lists, although the prefixes and suffixes used are inappropriate and may be used parentheses before and after the list or use a section marker as a suffix.

Likewise language specific Myanmar script consonant lists are unsupported, nor are doubled consonant lists.

Likewise ELreq has more detail on lists and counters: http://w3c.github.io/elreq/#x3-5-lists-and-counters

The implementation of this feature would allow other Google products such as Google Docs to display customized heading style.  Please consider this feature implementation this year.

And if the developers do not wish to add @counter-style can we at least expand the number of defined list types. A couple of hundred more (as a conservative estimate) should do it.