Sadly it seems to fail bad on things that aren't new articles.

Try for example https://en.wikipedia.org/wiki/Functional_programming/ as an input to smmry - you don't get the idea

I mean, it works ok. I think the issue here is structured documents like that wikipedia article. If you used smmry on each section, leaving the headers and structure alone, you'd probably get a far more 'coherent' result, and it's not surprising that the tool is built for "single block" content.

It would probably not be very hard to build a mediawiki smmrly extension that does just that.