I know they exist but I've only ever seen one house with such a tap and that was a very well off family member. I don't think these are terribly common.
They're not so wildly expensive. a couple hundred bucks maybe. My mom got one years ago, and it's really convenient for quick pour-over coffee. Great if you're in a hurry. I use a moka pot at home, but the 10 minutes it takes to boil while I putter around the kitchen trying to remember my name are really the most worthless of the day.
Minor nitpick here, but it's a fact I found interesting when I heard about it. The water inside a Moka doesn't boil, you can indeed observe that the water coming out from the top isn't boiling. What happens is that the air that is left inside the bottom chamber expands due to the heat, pushing the water upwards.
We have a Quooker and I recommend them to all our friends who ask, it's more expensive than others (starting at around £1200) but it's incredibly well built, designed/created in an era of making things to last, and they seems to stand by that; you can get spare parts and they sell a service kit for £25 (last I bought it) with the filter that you can replace every few years if you want, but you can also buy the individual parts of system like a new tank, just the core/element, etc.
I wanted one but also baulked at the price, got a ~£200 drop ship special instead. I might actually prefer it to the Quooker tbh - it doesn't spit. (The spitting is apparently a safety feature, but guess which one I've burnt myself on...)
I'm not much of a tea drinker myself, but I make it for my wife, the Quooker tap dispenses water at 100°C which I believe is sufficient for tea, I can brew it quite dark and it keeps a good temperature after adding milk.
As for pre-heating, I tend to use it to pre-heat my wife's tea mug and my coffee cup before I brew with the espresso machine in the kitchen, by filling it part way for a few seconds and then pouring away; mostly to take the chill off, as our kitchen can be cold in the mornings.
I know there are lots of other cheaper brands but my understanding from researching several of them a few years back was that many/most of the cheaper ones won't keep up with the Quooker, won't be as reliable, and likely won't have the after sales support as a product from a company that specialised in that single product. There are the office ones you speak of but they're been weaker performing in my anecdotal experience of our office, and often come with service contracts.
Seems like good way to get third degree burns if you're not careful? I just put my water filled mug in the microwave (with a spoon in to avoid superheating).
I've put my hand under the boiling tap once, it hurt a bit but I wasn't burned. Someone told me it has some sort of atomiser mechanism in the tap when the water is ejected to reduce the chance of burns, but I haven't looked into it and I'm not sure how true that is.
It's a quite deliberate and slightly difficult action to activate the boiling water, there's a ring around the base of the spout that you have to double-press and twist on the second press, completely independent of the normal cold/hot water.
I have two young children and honestly, I'm not concerned either for them, my wife, nor myself that there's any risk.
Using the microwave is a perfectly good solution I think, but I don't know many people who do that, and although it's fine for tea etc for one person, it won't do a house-full of cups of tea in seconds, nor fill a pan with boiling water.
I wouldn't dare to suggest that it's the best thing for everyone, but we are extremely happy with its utility in our home.
I know they exist but I've only ever seen one house with such a tap and that was a very well off family member. I don't think these are terribly common.