I noticed that the "Clear button" are usually found in search fields:
Why is it so uncommon for this button to appear in other input fields. For example this small configuration form:
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Clear buttons are normally provided when the field is being used affect a default view and the user is likely to want to return to that default. For example, to filter the list of all products in a catalogue and then to return to the unfiltered list. It's easier and more intuitive to click an explicit 'clear' button than it is to highlight the contents, delete it and then re-submit the form.
In other contexts that don't involve immediate changes to the view (e.g. basic enquiry forms), it's often just as easy to highlight the contents of a field and delete it. You could perhaps argue that it would be useful on touch devices where highlighting and deleting is more tedious.
It also doesn't make sense to include a clear button on mandatory fields (fields that cannot be left blank).
There are two common patterns for clearing:
The implicit clearing pattern improves efficiency. So I try to use it as much as possible, but only if it is not relevant to edit previous data.
If editing previous data is required, it does not alter efficiency to provide a small clearing button in the input field, so there is no reason not to provide it.