FYI this is effectively the XForm open selection, specifically:
... In this case, control select may have attribute selection="open". The form control should then allow free data entry, as described in 8.1.2 The input Element. The form control may permit multiple values to be entered through free entry.
which applies to both select (select_multiple) and select1 questions. Unfortunately, ODK Collect and Enketo do not currently support specifying selection="open" on selects. Instead, you can accomplish a similar result by adding an additional option - eg "Other" - and using this to trigger showing a following question to enter the custom value, as described here.
Which is to say, there is already a pretty well-established workaround for the absence of XForm open selection support in ODK [sic].