One of the biggest problems with delivering live events on Internet is 'scale', and TCP doesn’t scale well. For example when you are beaming a live football match -as opposed to an on demand movie playback- the number of people watching can easily be 1000 times more. In such a scenario using TCP is a death sentence for the CDNs (content delivery networks).
There are a couple of main reasons why TCP doesn't scale well:
One of the largest tradeoffs of TCP is the variability of throughput achievable between the sender and the receiver. When streaming video over the Internet the video packets must traverse multiple routers over the Internet, each of these routers is connected with different speed connections. The TCP algorithm starts with TCP window off small, then grows until packet loss is detected, the packet loss is considered a sign of congestion and TCP responds to it by drastically reducing the window size to avoid congestion. Thus in turn reducing the effective throughput immediately. Now imagine a network with TCP transmission using 6-7 router hops to the client (a very normal scenario), if any of the intermediate router looses any packet, the TCP for that link will reduce the transmission rate. In-fact The traffic flow between routers follow an hourglass kind of a shape; always gong up and down in-between one of the intermediate routers. Rendering the effective through put much lower compared to best-effort UDP.
As you may already know TCP is an acknowledgement-based protocol. Lets for example say a sender is 50ms away (i.e. latency btw two points). This would mean time it takes for a packet to be sent to a receiver and receiver to send an acknowledgement would be 100ms; thus maximum throughput possible as compared to UDP based transmission is already halved.
The TCP doesn’t support multicasting or the new emerging standard of multicasting AMT. Which means the CDNs don’t have the opportunity to reduce network traffic by replicating the packets -when many clients are watching the same content. That itself is a big enough reason for CDNs (like Akamai or Level3) to not go with TCP for live streams.