However, the space elevator is still incredibly viable in other locations. Small moons and large asteroids which have gravity but no atmosphere or space trash are ideal for space elevators. Since a space elevator can run off of electricity and is not limited by refueling or controlling explosions, it is far more reliable as a method of shipping items to and from orbit around a body.
The body most ideal for the first true space elevator will likely be the Moon. The Moon is a clean, fresh, low gravity environment which will undoubtedly be the base of most commercial mining and transport, due to its proximity to Earth and content of materials like Helium-3 and even water ice. The Moon will also possibly act as a spaceport to asteroid mining operations and even Mars colonization.
While rockets can be launched from the Moon easily they are still using consumable fuels. The need to use materials and weight to get something from the surface to orbit or vice versa is a waste. Rockets also break down easily, and are limited to a frequency of travel based on refueling operations and repairs. A space elevator has the potential to run off a clear view of the sun, is a simple machine compared to a rocket and is able to work 24-7 going up and down. Not to mention the fact that it is a fixed point of operations. It will always be in the same place ensuring there is no danger of missing a landing pad and hitting a habitat.
The construction of a space elevator is not as simple as just landing rockets however. The basic idea is to anchor a cable to the surface of the moon. That cable is then strung, from the surface, several thousand miles to a weight. This weight keeps the cable tight. It is similar to if you held a string with a ball on the end and then spun around. An elevator car can then run along the cable to and from orbit. All of this is possible with the materials available today. And while the set-up is risky and stringing several thousand miles of cable straight up from the Moon will be expensive, once established the elevator has little potential for problems afterward. And the cost to operate such a structure would be fixed over its lifetime just as the railroads are.
Essentially the group that owns the elevator would own the only bridge to the Moon. It would be in the same situation as the early railroads. A colony would grow around it and all commerce would move through it. An important consideration when finding a location for such a structure.
As a business it could begin by simply offering transport to the surface at a reduced cost and increased reliability to building a lander. But as time goes on it could just be a toll elevator. A fixed cost transport one direction or the other, though seasonal costs will likely be a factor.
The business danger to this system is similar to the railroads. If it doesn't run there is still the fixed costs of maintaining the system. Though we would hazard a guess that those costs would be minimal. Since the elevator comes into contact with nothing other than the vacuum of space environmental wear will be low. If used heavily enough it will require component maintenance but when that occurs the business will still be cash flow positive.
If the elevator were built tomorrow the real business challenge would be paying off the upfront construction cost in a timely manner while the industry catches up. Lunar mining will likely be the best solution since it can be performed autonomously and continuously. LiftPort is going this direction.
LiftPort is moving to build a lunar space elevator by 2020. The organization raised $100,000 on Kickstarter in 2014 to continue development of their design. They are intending to use a kevlar ribbon as the main cable of the elevator, which is the most vital and difficult component of the system. The elevator is meant cart lunar samples into orbit.
At this point LiftPort hasn't stated what the cost of construction would be. Though with possible launch costs and material cost it will undoubtedly be in the fractions of billions of dollars. If they succeed they will set a valuable precedent about the feasibility of the technology.
The space elevator continually appears in media as a technology to replace rockets on Earth. Unfortunately, there are just to many practical problems with such devices on our planet at this time. But space elevators are a very good idea in the correct areas. They are easy to operate, once built, and do replace rocket technologies with something more reliable. And while we have said many technologies will be valuable as businesses in the private space industry, lunar space elevators will likely be the most likely to succeed. Their superiority to conventional space transport is unrivaled from a technological and business standpoint. If a space elevator is built on the Moon those who own it will control much of the industry in that area. No one will swim a river when they can cross a bridge.
For more detailed information of space elevators see this NASA report on the technology:
The Space Elevator by Bradley Edwards Ph.D.