Whatamidoing: It won't solve the underlying problem. The issue is that it relies on ISO date which is deliberately limited. For instance it can't record any historical dates before the 1800s. The primary concern is that for a tool that is meant to serve multilingual wikis it fails to address the fact that there are several calendars (e.g. arabic, etc) currently in use around the world. It would be perfect if there was a single unambiguous calendar to denote all existing dates (both ancient and current), but such a convenient system doesn't exist. Dates are really complicated concepts.
George Ho: This extension is a bit like a documentation manual, it only specifies how things must work but it can't do anything to actually require that tools that implement it work that way. So while it certainly needs a way to determine how to format dates, or even specify different calendars it is up to each editing tool to implement it properly.
However, the request for adding just month and year needs to be logged in the specific extension talk page or the bug tracker because the ISO standard already supports it.