What is the StreamableHTTP transport and why does MCP need it?

The StreamableHTTP transport enables MCP clients to connect to remotely hosted servers over HTTP, unlike STDIO which requires both parties on the same machine. This opens up public MCP servers that anyone can access over the internet. However, HTTP creates a fundamental challenge because it is designed for clients to request from servers, not the reverse. StreamableHTTP uses a workaround involving Server-Sent Events to enable server-to-client messages that MCP features like sampling and notifications require.