Hard as stone is probably meant in a figurative sense, not a literal sense. End-grain wood is pretty hard, especially when compressed (for instance: by beating it with a hammer), but it is nowhere near as hard as stone. That said, there are some pretty soft stones :)

I've broken more than one high quality steel bit on various kinds of wood, but that's usually not a measure of how hard the wood is but how much friction there is between the drill and the wood and how much of the drill bit is inside the wood. If the wood were really hard you would not be able to enter the bit at all and it would never break but just sit there spinning on the surface.

Finally, the whole trick to a cutting board is that end grain wood will wear very little and the knife will be sharp much longer specifically because it is not as hard as stone.

Yes, many Chinese chefs and households still do use wooden chopping boards. I am not sure if the boards are as hard as stones, since there are many different kinds of stones. But thickness and the type of wooden do matter and will certainly make the wood very hard to crack (and to burn).

Here are some videos for the readers:

https://www.youtube.com/watch?v=oTNVDH6ZFLg

https://www.youtube.com/watch?v=isFTIHy7Duo

You will see pork bone chopping (beginning of the video), skin slicing (1:40), and meat grinding (5:30) in the second video.

Those are very typical boards in a restaurant's kitchen. The typical household chop board is a lot smaller and thinner, probably around 35" wide x 5" high. However, many families have moved away from wooden chopping board because plastic boards are easier to clean.

As far as resistance to bacteria, that will fall short with science. The passing down from generation to generation is a cultural effect. If you live with your in-laws, the board will of course be reused. Since wooden boards don't crack for years, yes, the board will be passed down. Butchers (Chinese and other cultures) use wooden boards because of the durability (Chinese chefs love chopping real fast with force). Real chefs prefer wooden chopping board (yeah, your famous Gordon Ramsay!)

Also, it is very common to see a butcher or a chef to stick the big kitchen knife on the side of the board tilted like the Leaning Tower of Pisa :-) The strength of a real butcher or a real chef can be so much more powerful than a MMA boxer.

EDIT: If you want a short English intro on this topic, https://www.youtube.com/watch?v=gDdoht0e1sg is solid.

Doesn't having a cutting board as hard as stone defeat the purpose of having a cutting board?

Isn't the point of a cutting board to protect the counter top from the knife, mobility (move chopped food to another location) and being easy to clean? As opposed to a flat counter top which can get marred with marks, can't move, can be cleaned but not thrown in a sink.

I'd say a much more important purpose of a cutting board is to protect the edge of your knife. If you hit the edge of your knife on something really hard, it'll chip, or fold--basically just ruin it. This might not be such a big deal for home cooks with super dull knives (after all, glass cutting boards still exist for some reason!) but for a professional I'd think a cutting board that destroys your knives would be worse than useless.

They also protect the knife blade from damage: if you were to cut directly on stone, the knife hitting the stone would cause it to dull more quickly.

Also to provide a less damaging surface for the knife blade.

My guess is that these wood boards would have much less friction than a stone equivalent, unless you had enough money to pay for a polished one.

The purpose of a cutting board is to protect the things underneath it that are not as hard as stone.

Then you could just use a metal plate or glass, but we use the wood in order to protect the blade of the knife also. You'd have to re-sharp the chef knifes every few minutes if they were used on the surface harder than the blade.

You should, and it's called steeling.

There's a foil edge on very sharp knives that will wrinkle and fold after use on anything, even tomatoes, making the knife feel dull. It's not, and it doesn't require removing metal as with grinding or sharpening, but you can steel to realign that edge or strop to hone it depending on the blade and angle. Even if you don't work with blades often, you've probably seen this depicted in media.

It really doesn't matter what the cutting surface is to the knife if you have great technique. Since I don't always, I use thin, flexible plastic barriers. I would never recommend wood outside of having no other choices or using it as part of presentation, mainly because of cross contamination and difficulty in sanitizing if you cook sous vide or serve raw often.

Obviously I meant the stone sharpening, not using the knife steel. And as for the material, many sources say that plastic actually contains more bacteria and that end-grain wood is more gentle to a blade than plastic. On the other hand plastic is easier to clean when it's new, but it's also more prone to cuts than wood and they quickly get dirty (at least in my limited experience). IMHO every board needs to be scraped or sanded from time to time to remove the top layer completely, that's the only way to keep it clean.

You'd destroy your knives/cleavers with a stone cutting board. The wood needs to give a little bit so the blade doesn't chip and holds an edge long enough to be useful. Sounds like pop writing sensationalism, as with Damascus steel, which TV shows imply (or outright state if they have no shame) is better than any steel we currently know how to make.

Bamboo cutting boards are often advertised as having anti-microbial properties. No clue if there's any scientific backing to the claim, though.

My experience with bamboo is that it's far more vulnerable to mildew than similarly-utilised wood items.