Here's the update in 2020: The mistake here is the assumption that bandwidth is 0.18c/GB, even if it's much less now on many platforms lets ignore this.
There are server hosts all over the world which offer unlimited bandwidth on dedicated servers such as servers.com. Additionally cloud providers such as DigitalOcean provide 1TB of free data per droplet you host with them, put your dev environment and some other side projects in there and you can quickly enjoy 5TB+ of free bandwidth including CDN.
If you really want to operate a video based platform and grow it without correlation to your billing the answer is as simple as purchasing your own rack mount or leasing a dedicated. The key to this, in the event that the site becomes popular enough to demand an infrastructure upgrade, is to prepare your framework and build from the ground up with the ability to migrate expeditiously, think kubernetes and the like.