You might wish to include it with “protection”, but in some cases the glaze also seals ceramics which are otherwise porous and would allow liquids to seep through (earthenware). This isn’t an issue with porcelain, which is already quite non-porous - they don’t have to glaze the inside of the toilet tank.
I just bought a “bone” (basically, beige) colored toilet at Home Depot. It cost about $5 more than the identical white one.
A bar I used to frequent in Chicago’s loop had jet back fixtures: toilet and sink. Freaky but cool…TRM
You want fixtures that are hard to find in any color other than white? Try urinals. I’ve been in a bunch of public restrooms where the toilets and sinks were some fashionable color, but I’ve only been in one restroom where the urinals were not white. I know that you can get urinals in other colors - the Kohler showroom has a few. But almost no one puts a urinal in their home, and as it’s been pointed out, few restaurants/gas stations/hospitals/etc. are going to pay extra for fancifully colored fixtures.
People prefer white specifically because it does show when it needs to be cleaned. This is not simply a case of looks, there are health issues associated with dirty toilets.
So the predominate color is white because of market pressure. However some companies like Kohler offer about 20 colors for their toilets. One of the more popular brands, Toto, offers several colors as well including black.
My old boss had black toilets in his condo. No idea how clean he kept them but they always icked me out because god knows what could have been masked by the dark coloring?
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The ash-tray and candle-holder are wonderful touches.
It needs a magazine rack. For almost $10K you’d think they’d have thought of that.
Definition provided for those unfamiliar with the term you used.
You’re welcome. 
Mine is brown. It was white when we installed it though.
I used a black urinal at a truck stop just last night, and my thought was that’s a good idea.
And yesterday afternoon I used a really weird one. It didn’t flush. There was no running water. And it was near a play area for children (sign on the door said “boys” not “men”), but it was mounted high enough that I had to step back and aim upward.
Granted, we’re not talking “public” restroom here but the guest toilet we have downstairs at home is black porcelain and IMO when it’s clean it’s every bit as apparent as with one that’s in white. You can tell there’s nothing lurking because of the lustre despite the non-white color.
I don’t know if toilets can be elegant but I think black ones come about as close as you could reasonably expect. Black porcelain positively shines with regular maintenance. They’re just like black cars; they show dirt easier than a white one will and (IMO) look better when they’re clean.
Ed McMahon had one made out of gold! 
The last time I was in the hospital, the sheets were blue. And the bottom sheet was a fitted knit sheet. I had MRSA, so my linens definitely needed to be bleached, but I had blue sheets.
Note too that a bell rings when you flush. Basically, therefore, every time you drop a log, an angel gets his wings.
Our house had a brown toilet until we replaced it with a white one. Based on the OP’s reasoning, a brown toilet (it was “shit brown”, in fact) would be perfect. It wasn’t. It was difficult to tell whether one of the kids had forgotten to flush or whether it needed an extra flush to wash away “remnants”. After too long without cleaning it, you could see a film starting to form in the bowl. I assume that the same film grows on white toilets but isn’t easily seen.
Our upstairs bathroom has American Standard fixtures in “Ming Green.” The green is, of course, a thin layer over the top of the naturally white or off-white porcelain, so even the smallest chips in the finish are very very visible.
Fascinating article from Old House Journal on the history of colored bathroom fixtures: In Living Color: The bathroom goes from austere to eccentric.
Was it one of these? They use a layer of lighter-than-water (presumably lighter-than-pee as well) liquid to provide a barrier between the waste and the outside.
I recall another Doper commenting that these are likely to be a plumber’s nightmare, precisely because they don’t flush. Without the periodic flow of water, salts from urine are much more likely to crystallize and block the waste pipe.
Jeez you guys. Toilets are made from kaolin clay, which is white. Any other color (and you can certainly get any other color you want) is an admixture, either to the glaze (otherwise clear) or to the clay.
White is the unadulterated default. And for many reasons, in many but not all circumstances, preferred. But pick whatever you want!