It does, which is why it'd need to be Javascript as the HTML including the iframe returned by the oembed API is in json. The Javascript probably isn't that complicated to make the API call, extract the HTML and update the page but to do it well (so it doesn't block the page, works with lots of embeds, etc) isn't something I know how to do.
I did find this:
https://embed.ly/
I'll probably play around with that a bit to see how it is but I suspect that the # of page views we get is way above their cheap tier.