What problem does this address?

The Patterns inserter surfaces header and footer patterns that may have already been used to create template parts at the site. Consequently it's very easy to insert a pattern in a template where an existing template part might be preferable.

What is your proposed solution?

If we list existing template parts in the pattern inserter we can hopefully reduce the likelihood of such occurrences. We'd need to ensure the UI clearly distinguishes patterns / template parts.

A couple of ideas to kick off discussions: