I'd expect "local MCP servers" will be generally installed as part of something else. Photoshop, or Outlook, or whatever could come with a local MCP server to allow chat clients to automate them. Maybe printer drivers or other hardware would do similar. I don't think there's much reason to install a cloud service MCP server to run locally; you'd just use the one provided in the cloud.
Interesting thought.
But maybe the companies would actually like to at least pipe the communication throught the cloud to get all the usage data. Here's one possible architecture:
local chat client
local MCP server provided by company local tool (for example photoshop)