I went down the road to save my ombied results in db. I use the embed.ly service to get my oembed objects, and although the response time is generally good, caching responses in db greatly improves client performance.
I also set up a service that runs once a day (it seems enough) and updates db-cache once a day.
One thing that can become a problem is getting oembed with a given size (e.g. max-width). Changing the built-in html / flash to another size on the fly will not be funny ...
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