A TURN server has to do much less computation, and it also doesn't need to decrypt the payload. It's more or less a fancy packet forwarder.
In addition, only a fraction of users will need TURN; the rest can use direct peer connections with the aid of NAT traversal; the two kinds of connection are more or less the same to higher layers. Conversely, if the application depended on an application server to process data, chances are you wouldn't implement a second version of the same protocol that works without the server.
So a single TURN server can handle a lot more traffic than an application server, is potentially more secure, and is more easily shared between different applications, and even different owners.
If you want it geo-distributed for latency, the ability to share the same TURN servers between different applications and owners gives you cost-latency advantages too.