I'm not well versed in anti-trust law, but how does Youtube's popularity (monopoly as you put it) prohibit you from hosting your content on the 100s of other video hosting services available to you? How does Youtube's popularity prevent you from hosting your videos yourself?

You're expecting them to use their own money and their own resources to broadcast messages they don't want to broadcast, for free.

> How does Youtube's popularity prevent you from hosting your videos yourself?

It doesn't. It "prevents" most people from looking for videos anywhere except the youtube search bar.

> You're expecting them to use their own money and their own resources to broadcast messages they don't want to broadcast, for free.

Well, does that prevent them from starting another business, that doesn't seek to grow so big and pervasive that it should be considered common carrier?