Sometimes the singular is lexicalized: we don't say *teethbrush or *feetrest because the words toothbrush, footrest exist. Otherwise the singular sounds a bit more natural to me: mouse eater, mice eater, tooth treatment, teeth treatment; and these are in sharp contrast to the unacceptable *hands rest, *rats eater.
Seen in a supermarket: a bunch of white woolly things labelled 'feet warmers'. An illustration of the morphological principle that irregular plurals can be used as modifiers of other nouns, whereas in general usage regular plurals can't: *hands warmers.
Note: 'sports' is one common exception in general usage; business and law parlance freely use plural modifiers ('securities expertise', 'notes issuance').