Performing an HTML substitution from AjaxResponse rather than using a wrapper
So, I used the source, and I found out that Drupal\Core\Ajax\ReplaceCommand calls getRenderedContent(), I found an implementation in CommandWithAttachedAssetsTrait where I saw that it expects an array, as I should have well known. So I ended up with the following calls:

$response
  -&gt;addCommand(new RemoveCommand('label[for^="edit-struttura-input"]'))
  -&gt;addCommand(new ReplaceCommand('input[id^="edit-struttura-input"]', array( $form['struttura-input'] )))
  -&gt;addCommand(new InvokeCommand('#edit-field-next-field-to-edit', 'focus')  )


Note that I removed the wrapper, as suggested by @4k4, but then I had to select on a match on the start of the ID of the element, and to remove the label, since it is added by each new rendering. As a command to get rid of the datepicker I simply moved the focus to the next element to edit, which is very convenient to the user.