Easy way to remove search filter

Current

Proposed

Note the presence of a 1-click option to clear the search box, while still maintaining the existing functionality.

Exceptions

This doesn't have to be everywhere. Only persistent search boxes. For example, in the global search Ctrl+K the search box that comes up does not keep its value between invocations. It would not need a clear button; it would be bad if it was changed to remember its state.