Is it that expensive these days? Specifically, Cloudflare R2 has free egress, so you pay a fraction of what you'd pay most other places for the underlying "serve video" part of a platform.
The Cloudflare TOS does not allow you to serve video from a Cloudflare address unless you’re using a Cloudflare product that is meant for video. So no, you can't make a youtube clone and make Cloudflare pay that bill for you.
Cloudflare makes their money by making users overpay for other things than egress. Video hosting is one of the exceptions where they can't make up that on other costs which is why they have another service for it.
Nobody is taking the weird of one message posted in a medium as non-discoverable as Discord as enough legal stability to build a YouTube competitor on.