That's exactly what I do, but with an additional IE hack - it works great:

.embed-container {
position: relative;
padding-bottom: 56.25%; /* 16/9 ratio /
padding-top: 30px; / IE workaround*/
height: 0;
overflow: hidden;
}
.embed-container iframe,
.embed-container object,
.embed-container embed {
position: absolute;
top: 0;
left: 0;
width: 100%;
height: 100%;
}

Thanks for posting this, guys! Can you send a pull request? If you need to learn how, check out this tutorial:
http://docs.joomla.org/Git_for_Coders

Thanks for reporting this. At this time we are only using github as the place to submit code fixes so I am closing the report here. The actual reporting of issues and testing fixes is still taking place on Joomlacode.

As it has been some time since you opened this issue can you please confirm that it is still valid with the current Master or Joomla 3.2 beta.

If it is still valid please can you open an item on the Joomlacode tracker in the appropriate area.

CMS Bug Reports: http://joomlacode.org/gf/project/joomla/tracker/?action=TrackerItemBrowse&tracker_id=8103

CMS Feature Requests: http://joomlacode.org/gf/project/joomla/tracker/?action=TrackerItemBrowse&tracker_id=8549