The native app that allows for MCP is only available officially on Mac's and the web interface is generally more convenient for non-technical users. Searching and interacting with the web has become a table-stakes feature and was a glaring gap in Claude.

Let me rephrase it.

MCP has the capability to add this functionality.

It would be nice to see MCP getting adoption in their web UI, as well easier UX, rather than more ad hoc features being added natively.

This is likely implemented behind the scenes as an MCP server exposed to their model in the web UI. It is likely that they will enable MCP servers over HTTP+SSEs (vs the stdin/stdout used with Claude desktop) on the web version in the near future.