Interesting experiment!
I think tool calling (such as MCP) is really underrated. People think of it as a way to connect to Google Drive etc but the potential for MCP to power actual in-chat apps is very under-explored.
I've been working on something called Liveclip which is like tables in chat: just a few hours ago I implemented a way for ChatGPT (etc) to surface sentences within the US Constitution: https://x.com/firasd/status/2049187034066198658
I've also thought that games are an obvious way to explore chat-native MCP apps. Hangman for example. Also small utilities like a clock. In fact I have a no-auth remote MCP clock that can be added to any client right now deployed straight from https://github.com/firasd/mcpclock to https://mcpclock.firasd.workers.dev/mcp <-- works in Claude .ai, Claude iOS, Claude Code, Codex, etc right now