Could we maybe switch over to YouTube's "new" way of embedding content? Because the old way is a) deprecated and b) relies on Flash solely which should be equally deprecated.

https://developers.google.com/youtube/player_parameters

The new method detects the method to use and offers either Flash or HTML5. With Browsers like FireFox disabling Flash completely and Edge offering a pretty prominent "Disable Flash Globally" option, this would be the way to go.