I'm one of those people who really doesn't like these kinds of x-sharing services when they're just breaking the law. But when they aren't I'm all for the competition and additional money making opportunities it creates for participants.
I'm getting ready to go on my 3rd multi-week trip with housing provided almost entirely by airBnB. So far I've been generally very pleased with most of the hosts. In general, I've found the ones outside of the U.S. tend to provide a better experience per dollar than in the U.S. I've also found myself at some delightful B&B's who just list on AirBnB instead of other methods. On the other hand, I've also found myself in some sketchy group home like experiences with no owner to be found (mostly in the U.S.).
The hard part of it is this, I can put together a multi-location road trip across six or seven countries in a few short hours on AirBnB because all of the "vendors" list there (many times faster than doing it with hotels), and the total price will be 1/2 to 1/3rd the price of doing it in hotels, and the quality of the experience will be about on par with any 3-star hotel I'm likely to find. I've yet to break $70/night on AirBnB (for entire flats/apartments) because there's usually so much inventory. The locations can be better than "hotel districts" and I can usually find something very custom and suited to what I want.
The reviews also reinforce the honesty of the listing, whereas hotels will show pictures of a model room with idealized lighting and the reality is often not the same. Bonus, we've often gotten to talk with pretty interesting people, seen interesting neighborhoods we would have ignored before and use public transport much more fully than we would have otherwise.
I think the easiest way for hotels to compete against AirBnB is to simply start listing on it and competing, room-for-room. Room 607 in the local Marriott has a noise problem? It'll show up in the reviews. Front-desk clerks rude in the Albany, NY Holiday Inn? It'll show up. Prices too high for what you get? It'll have to compete against local housing inventory.
I'm also very sympathetic to many of the comments here regarding areas with very high housing prices. In terms of local housing strategy, simply banning these kinds of services should be part of a local multi-pronged strategy to reduce housing prices (along with limiting other investment options). But I'm not so sure it's a universal problem. Every time I've booked big trips on AirBnB I've always found hosts who are renting out multiple properties and don't live in most of them. However, in many cities, looking at the rates they're charging, they're not suffering from the same kind of systemic housing shortages places like SF or NYC are.
One other thing to consider in tight markets. If the local municipalities aren't going to restrict investment ownership, AirBnB may end up being a better user of the investment properties than people who simply buy up properties and they lay completely abandoned for years. Because the market that AirBnB has to work in is different than say, foreign investors, it also might help better shape the kinds of properties that get built to eventually be more affordable. e.g. 432 Park Ave is going to end up mostly uninhabited even if the "tenancy" is at 100% and none of those apartments are going to end up on AirBnB. This inventory of $30million dollar apartments is not going to go anywhere. But AirBnB investory might be on the lookout for more affordable construction to invest in, knowing that someday they'll sell the property off to more regular buyers and need to rent it to normal people as well in the meanwhile.