Why does horizontal scaling create problems for stateful MCP servers?

When an MCP server becomes popular, you need multiple instances behind a load balancer. But MCP clients maintain two connections: a GET SSE connection for server-to-client requests, and POST requests for tool calls. With a load balancer, these may route to different instances. If a tool needs Claude through sampling, the instance handling the POST must coordinate with the instance holding the GET SSE connection. This creates a cross-instance coordination problem that standard load balancers cannot solve.