In the case of Vidyard content, we use a global CDN to cache and deliver content more quickly so that we can better ensure smooth performance and push important updates in a more timely manner.
While local caching may potentially decrease load times by a small amount, it could also produce issues if changes were made to the player after content was cached since an older version of the script may be running on the browser.
That being said, our team are always looking to streamline the playback and loading experience to help speed up performance in general.
If you do wish to defer overall script loads on the page, we do have some sample scripts which can be used to load a player on demand after the initial page load which may help with your situation.
Feel free to pass these examples on to your development team to see if either option may benefit your use case: