There's a problem, however, and it's with devices that have no Flash. On those devices, the embedded video simply disappears:
On my actual device, actually, the "ghost" window doesn't appear at all; there's just some vertical space where the video should have been.
Flash-less mobiles, however, are perfectly capable of playing Youtube videos — I just have to follow a link to the relevant Youtube page. (This is, among other reasons, why my original proposal didn't go as far as actually asking for Youtube embedding.)
Is there a way the embedded video block can be replaced with... something else, when Flash is not available? Even just a bare link would do.