The real problem is that the Internet is made up of many different ISPs which are connected together. Each ISP is independent and negotiates any connections with other ISPs. Multicast comes in two basic flavors: DM (Dense Mode) and SM (Sparse Mode).
In DM (and at the start of, and periodically during, SM), multicast is flooded across every router and router port. This just isn't practical to do on the Internet, and ISPs which have nothing to do with the source or ultimate destinations of the multicast traffic would be forced to carry it, using their precious bandwidth for no reason.
SM initially, and periodically, floods the way DM does, but it will eventually back off of sending multicast traffic everywhere. That requires an RP (Rendezvous Point) for each multicast group. Someone would need to purchase and maintain these RPs.
Also, there are a limited number of multicast groups. The groups would need to be registered and assigned to companies the way IP addresses are. In a global multicast, only one assignee in the world could use a multicast group at any given time.