Yes. But in order to do that you run the MCP server for that API locally. Is it really worth doing that just to have the additional /list-tools, when it is otherwise basically just a bridge/proxy?
Check out the overview in the MCP spec. Locally you run the "host application" (e.g. ollama or Claude Desktop). Then you have clients which are inside the host application and maintain 1:1 connections with servers.
Then you have servers, which are separate processes running on your machine that the clients connect to. For example, you program a server to "manipulate your local filesystem" in python and then run it locally.
Most MCP servers are written for python or node and to install and use them you run them locally. They then are like a "bridge" to whichever API they abstract.