You absolutely can make a local MCP server! I use one as part of TalkiTo which runs one in the background and connects it to Claude Code at runtime so it looks like this:
replytalkito: http://127.0.0.1:8000/sse (SSE)
https://github.com/robdmac/talkito/blob/main/talkito/mcp.py
Admittedly that's not as straight forward as one might hope.
Also regarding this point "letting you easily connect to your own Agents SDK MCP servers deployed in their cloud" I hear roocode has a cool new remote connect to your local machine so you can interact with roocode on your desktop from any browser.
`tailscale serve` is easy.
Set appropriate permissions/credentials to authenticate your ChatGPT to the MCP.
replyAgreed on this. I'm still waiting for local MCP server support.
replyOne way around this to use a gateway to run the local MCP - then connect to it via the gateway. We just rolled out support for that [1] in the one we're making at mintmcp.com
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