I'm not sure if this idea is even reasonable, but let me try it out anyway.
It would be cool if a wiki's users (probably admins) were able to
define stuff to be part of the API. (Actually I'm thinking more of
being able to define custom RSS feeds, but they're somewhat similar
ideas, I think.)
Two typical examples would be page of the day and image of the day.
Wikimedia wikis already have systems set up so that (e.g.)
[[template:potd]] automatically shows that day's 'picture of the day'
(by parser functions).
Maybe the API could read a page [[MediaWiki:Custom API]], whose
contents could be like this:
* [[template:today's featured article|dailyarticle]]
so then maybe API users would be able to do
and they would get the content of [[template:today's featured article]].
I don't even know if this is even remotely feasible, but it would be
super cool if it was.