Why are bathroom sinks made of porcelain while kitchen sinks are made of metal?
Lots of bathroom sinks are made of metal (mostly high end sinks) and lots of kitchen sinks (including mine) are made of porcelain. Some folks don’t like porcelain kitchen sinks because they can be chipped by heavy pots or pans that are mishandled. That’s generally not an issue in the bathroom.
I used to work at a kitchen and bath store selling plumbing fixtures. To the degree your OP is true, it’s just convention. In my person experience selling a LOT of both, your premise is flawed. High end kitchen sink sales are just as much porcelain as they are SS.
When I was a kid, the kitchen sink in our house was at least porcelain-clad. One day my dad was helping my brother with a science project about thermal stress. He put a couple of marbles in a skillet, and heated them in the oven to about 500F. While they were baking, he put a couple of inches of ice water in the sink.
He then dropped the hot marbles into the sink. One of them shattered. The other one went ping! and chipped the porcelain. Thermal stress works! 
Had the misfortune of having two metal (enamel-coated) bathroom sinks (and ditto kitchen) when we moved here. Did not wear well and, of course, eventually started to rust out. The kitchen sink has been replaced twice: the first with “Americast” (very bad idea) and now granite-crete type stuff. The bathroom sinks are porcelain-ish.
Metal kitchen sinks are generally stainless steel, sometimes treated to other colors. Stainless steel bathroom sinks are not as common but available. You can get copper, etc. ones.
Kitchen sinks are used for washing dishes and dropping a heavy dish could easily crack the glaze or the body of the sink. The term sink derives from ‘zinc’, early wet sinks were made of wood and lined with zinc. Bathroom sinks started as porcelain bowls. Porcelain kitchen sinks are large and heavy, and expensive, but coming back in style for a retro country look. Both types are available for kitchen or bathroom though.
In the UK stainless steel is the overwhelming choice for kitchen sinks and porcelain for bathrooms. Porcelain kitchen sinks are large and heavy, and expensive, but fashionable. In my experience the risk is more to the china plates than to the bowl. Vitreous enamel sinks are also popular because they come in a variety of colours.
One of the most popular kitchen sinks these day is the farm style sink. It can be stainless, but is almost always porcelain.
Similarly, one of the trendy bath sinks is the vessel sink. Can be stainless, copper or nickel or almost anything. I’ve even seen wooden sinks (it’s the Big Sur look).
I have an older home, at least 60, and possibly closer to 100 years old. It has a battered, stained, but still functional white non-metal sink in the kitchen.
I suspect the popularity of stainless for kitchens is partly because of the ease of cleaning. No amount of bleach or scrubbing is going to get my kitchen sink sparkling white again.
Style is also an important factor. For those wanting a more traditional look in their kitchen, porcelain is the usual choice. For those wanting a more contemporary look, stainless is the way to go.
This. My last house had a heavy porcelain kitchen sink. If you dropped any porcelain cups/plates/bowls into the sink from more than an inch or so, they shattered as if you had dropped them on a concrete sidewalk. With a stainless steel sink, they’re more likely to just bounce (unless you drop them from quite a bit higher).
The toilet, on the other hand, seems to always be porcelain. I guess it’s hard for a metal commode to develop cachet when that’s what they use in prison.
Definitely true. But if you drop a cast iron pan in a porcelain sink it’s usually gonna be the sink that suffers.
A stainless sink is going to be dented, too.
That’s in part because of the matching sets: normally, people will get a matching toilet sink and throne, even if the shower or tub do not match. Another place where you get toilet sinks in metal, along with a matching throne, is in transportation (planes, trains and buses).
Plus “praying to the stainless steel god” doesn’t have quite the same ring to it…
FWIW my kitchen sink is Corian and by bathroom sinks are cultured marble…
Not the case. The origin of ‘sink’ traces back to PIE. Unrelated to ‘zinc’.
Curiously, their original meanings are almost antonymous: sink as a depression, zinc as a point or spike.
brainstall, there are companies which refinish bathtubs and, at least, bathroom sinks. I believe that it is an epoxy coating so I don’t know how durable it might be. You might call one of these companies and see if they might do your kitchen sink. I am also, not sure what the cost might be.
Bob
I see that. Old wood wet sinks were lined with zinc, but I don’t recall where I saw that explanation for the name now. Oh well, live and learn.
It could if you dropped it hard enough, but a stainless steel sink will stand up to the impact without denting far better than a porcelain sink would without cracking. A small dent won’t ruin a stainless steel sink, once the glaze is broken on the porcelain sink the ceramic underneath can start to degrade, although it takes a long, long time before a single small crack would matter.