Many clients don't know how to find it, how to control its display, or the fact that tokens are required to get it to display in the Teaser. The Markup also some times goes into the upper image field. Many also do not know that [embed:1], etc. work. Overhauling this functionality would be quite useful.
This is especially important on overviews, where simply adding [embed] into the overview body doesn't work and won't display reliably on landing pages. This makes using widgets almost unworkable.