Possible names for the category of "gravel bike that can accommodate 29″×2.25″ tyres":
Drop-bar mountain bikes
Rigid mountain bikes (if the stress is on avoiding all suspensions, rather than on using dropbars)
You can. The rim widths aren't stated but I'd be pretty certain you could go down to 35mm, and probably 32mm. Here's a rather cautious compatibility chart.
However I wouldn't do so until you've got the bike in your hands. The specs are nonsense so you can't be sure what you'll end up with:
"Frame: 700x40 max tire"
"Tires: Kenda 1052 ...
While other answers have pointed out some 4-wheel "bikes", TrikExplor make an off-road quad recumbent which can even be 4 wheel drive and have electric assistance.
Stick some fat studded tyres on that and it will be very capable indeed.
Parking won't be easy and I suspect the cost is bank-breaking given that they're built to order.
There is a Velomobile on 4 wheels.
And it can come with a child seat in the back.
I have heard about two seater velomobiles which have the second person behind the first but could only find pictures and websites with them side by side, making quite a big item which will likely not fit on the bike infrastructure where you live.
As all the ...
In addition to all the other answers: A trike or quad won’t fall over on slippery surfaces, but you can still lose traction causing you to crash or go off the road.
Unless you are going very slowly your forward speed is much more dangerous than the meter or so your center of gravity is above the ground. The mere act of falling off the bike is relatively ...
Local laws usually don't allow 4 wheel vehicles to be classified as bicycles, so that is the main reason you don't see them except at the beach and as rentals in larger parks. Equipping them for the road would require a windshield, safety equipment- on and on until it is too expensive to buy for use on the street.
The main downside to a quad wheel is keeping all wheels on the ground.
The surfaces we ride on are not flat, so there's always a situation where one wheel would be off the ground or at least lower ground-pressure.
If the bike has one powered wheel, then it can get hung up with the powered wheel off the ground. This can be reduced by adding a locking ...
Look into the winter road below (image credit), similar (little worse) than that I need to deal with:
A bicycle with wide, knobbed MTB tires can take the car spur on the right. It is not a very nice ride but it would work on lower gear. In my case, my electric engine will help me to pull through if not too far. But a tricycle would need to dig a thick snow ...
Trikes, particularly recumbent trikes, are relatively common and provide the kind of stability you're talking about--although they (and quads) are prone to flip in turns if you don't know how to corner. My impression is that whatever marginal advantage a quad might have over a trike is not worth the disadvantages.
Riding a trike or quad on a flat tire would ...
Why do they not sell bicycles with four wheels?
They do sell vehicles with four bicycle wheels.
As Carel said,
Two wheels is by definition a bicycle
Three wheels is a tricycle
four wheels is a quadricycle
Google "quadricycle bikes" and you can find a variety of small companies that make them.
Here is one example:
VierBike Sport Standard