I'm toying with the idea of setting up an MCP for my current company's product, even as a proof of concept. The product is an auth server.

But I'm not sure that is the right approach. My thesis is that configuring core infrastructure is less of an MCP task than making calls against existing APIs.

Put another way, would you rather ask Claude to set up an S3 bucket (quick but non-replicable, not version controlled, etc) or ask Claude to help you write Terraform to set up the S3 bucket (which could then be pushed into the normal gitops CI/CD infra management process)?

IMO, Both of it have its places, there are many small companies who don't do Gitops for them asking claude is better than navigating AWS console. For your case, why not ask claude to generate TF ,fix any errors and and run tf apply.

How do MCPs actually work, where are the real use cases, and the challenges today.

I don't think too many people are going to want to write the essay that would be needed to truly answer that. I would just point you to:

https://modelcontextprotocol.io/introduction

and/or any of the dozens of Youtube video introductions to MPC, to get a good feel for how it works, and how people are using it.