The ?embedplayer=yes in TimedMediaHandler has three main problems:

1. it's easy to erase (we're having problems with the WordPress blog erasing it from embeddings)
2. it only works on TimedMediaHandler stuff, but we want to be able to embed other media types probably, and this is a good chance to add something to core
3. it looks silly and is long

Recommend adding an action=embed instead for iframe-style embedding, and adding "/embed/$1" to $wgActionPaths in production.

Will flesh this bug out more in a bit.