Does a select input element (fixed options) need a "clear input" button?

In our custom select element the user can start typing a category.The option nearest to the typed text is highlighted and will be selected with enter, tab or clicking. The options list is fixed so custom input is not permitted.

This is the flow:

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The big question: does this input field need a "clear input" button so the user can see the whole option list again quicker? Or does this result in more errors (removing input that won't come back)?

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