Embedded YouTube videos don't work unless I un-proxy CF

I’ve found a few other people that have expressed a similar problem, but no resolution. The closest I could find was this thread from last year, where the answer was related to streaming video:

Then I found this, stating that CF doesn’t allow “streaming video content” because it takes up too much bandwidth:

It looks like the solution is to pay for CF Stream:

But this doesn’t make sense. I’m not streaming from my server, I’m just embedding videos that are on YouTube.

Do I have to pay for CF Stream to embed YouTube videos?