Is YouTube even profitable? Even if they are, it seems like the only reason cost could be "reasonable" is because they piggy back off of being Google scale (co-location, negotiated bandwidth rates, global network of self-hosted data centers). Not to mention the network and aggregate effects of having an existing ad market and user profiles for targeting ads.
One could probably mitigate high operating costs by charging for the service or limiting who can post on the site. But I think these two factors greatly contribute to YouTube's monopoly status.