If you connect the dots of the earlier MCP Client/Server docs you understand that your desktop AI tool was also a MCP Server. This MCP Server provided the tools like "search files", "alter files", "open file".

It's was simpler to design/implement the AI tool if these interactions had state. When this was generalized to internet interactions this no longer made sense and was gradually cleaned up.

I think at the same time, the AI tool "protocol" to interact with the local system moved away from MCP model.

During the initialize step, the client tells the server about its capabilities. Then the server remembers them for the session, so the client doesn't need to keep saying what it can do, and the server won't expose tools the client can't use. It's more overhead for the server, but more efficient over the wire for the rest of the session (that's just my understanding at least -- not saying this couldn't all be stateless).