Hi!
Well, I think we could sidestep the grammar issue by using unit symbols. We
True, but what unit symbol is "apple"? It's actually used as measure of height (bonus points if you can guess on which item :). Even if we don't go this far, while SI units probably all have short names, for non-SI units, especially older and rarer ones, it may very well not be the case.
Another tricky part is that short names are not connected to languages right now. I.e. if your interface language is Serbian, which short name to use? What if it's Farsi? We'd need to change how we relate units & unit symbols then.
An alternative is to use MediaWiki i18n messages instead of entity labels. E.g. if the unit is Q11573, we could check if MediaWiki:wikibase-unit-Q11573 exists, and if it does, use it. We'd get internationalization including support for plurals for free.
That may work, but downside of this is that it is linked to unit ID - so if we wanted to use it for, say, Commons data, we'd have to somehow link between "metre" on Wikidata and "metre" on Commons.