If you want to be picky shouldn't we then also refer simply to fallow, muntjac and roe? Are there any other creatures with the same name that aren't deer? Ever heard of a fallow sheep, a roe horse or a muntjac cow? Until the arrival of sika, referring to a stag needed no further identification any more than did hind or hart. Unfortunately, when sika were introduced to the UK nobody thought to bring with them the Japanese words relevant to the genders. Had they done so we would now be referring to sika stags and hinds using the relevant Japanese words. Google tells me stag translates as kuwagata although I cannot be certain that this is appropriate in its inference. Only with native European stags and hinds might we more commonly use the collective term deer, and only then if preceeded by the colour adjective. Deer, on its own, is as broad a description as cat or bird.
If pedantry is to rule then surely we must insist that fallow bucks and fallow does are referred to collectively simply as fallow, roe bucks and roe does simply as roe and muntjac bucks and muntjac does simply as muntjac. That would then conform to the practice of not collectively referring to the cocks and hens of various species as pheasant birds, partridge birds or pigeon birds and so on.
...and while we're on the subject, we in the UK always referred to the bass as just that. No further description necessary. Do we ever refer to sea mackerel or sea cod? No, we do not and neither should we need to refer to sea bass. Yet another Americanism that trendy, overpaid, thirty-something pasta cooks use in the absence of any real knowledge of traditional British fare.
I do not, however, suggest we shorten references to CWDs as Chinese Waters.
I know, its late and I've been up since dawn. Time for my tablet, the shipping forecast and the Land of Nod.