What the company is doing is essentially illegal. You can't rent out a living space without applying for rezoning, and then it still has to be with the approval of the city planning department of the city. You can't just let people turn their places into rentals. I live in a large city, and I would mostly agree that city planning in necessary in order to avoid problems with traffic, parking, and all the other problems that happen in dense urban areas.
I think the idea is great, but it's not going to work, maybe in a more relaxed country where they don't care to do any city planning, but not in the United States and other more densely populated cities.
I live in Singapore, where Airbnb will remain illegal for a long time. That said, is "that's illegal!"necessarily watertight proof that something isn't going to work? Could it be possible that people might like the idea of something enough that cultural attitudes change, and people demand different things, and laws shift and change to accomodate what people want?
The thing is, the reasons why Airbnb is illegal (e.g. the zoning laws that the parent mentioned) aren't really subject to shifts in cultural attitudes. It boils down to city planning and structuring (the flow of traffic, the layout of utilities, etc.), all (or at least most) of which are put in place to try and make our horribly inefficient cities just a bit more efficient.