Sadly, network effects. The same reason that eBay doesn't have any serious competitors, despite the awful experience they offer.

What's so awful about eBay? I have always been able to find pretty much exactly what I want at a reasonable price.

It's great for buyers. It's awful for sellers. They charge massive fees and offer virtually no protection against buyer fraud.

Try selling

The more relevant question is, what business plan is going to let someone with a similar website attract customers?

You have to find a weak point in Airbnb. Maybe focus on particular underserved cities. Maybe only allow amazing properties and aggressively poach them from Airbnb. Maybe try to enforce a common high-end experience by providing hosts with branded physical goods. Maybe piggyback on an existing hotel brand. Maybe market to the business market exclusively (worked for LinkedIn.) Just some quick ideas, and maybe not viable, but just cloning Airbnb isn't going to get you far.

Agreed. However, no one is going to compete with Airbnb anytime soon. To compete, you can't just be a little better, you need to be a lot better. Reason being, people have accounts on Airbnb, they have feedback, and they're familiar with the experience. If a slightly improved HN is released by someone tomorrow, we don't all jump ship, because we're invested in the current community. For us to leave, it would need to profoundly improve on the experience or offer incredible content. Likewise, to compete with Airbnb you would need a completely different approach or business model, or have a selection of apartments that are far beyond Airbnb in quality and affordability.

Airbnb pushes out updates frequently, their site offers a great experience to the user, and they have a solid team of developers that stay ahead of the game. They're going to be here for a while.

Airbnb already negotiates with individual cities to charge taxes for certain rentals (look at Portland).

As soon as they're big enough, they will start supporting these taxes and pushing for laws that require collection, as it makes it more difficult for others to enter the market the way they did.

Critical mass.

What would stop someone from putting their property up on multiple websites?

It's a rational decision for most sellers. There's a bunch of properties listed on AirBnB, HomeAway and VRBO (latter two being owned by the same company). For buyers I'd guess existence of previous transactions and reviews is a quality signal, as opposed to a site where you can get scammed by a dishonest seller.

There's also the niche differential. VRBO & Homeaway tend to be more for vacation rental properties (not all, but that's the trend).