Please do tell; Is it because of the strength of the nanotubes?
The manufacturing of such a long cable without any mayor faults?
The danger on the structure by weather micro meteorites and normal space radiation?
Without any major faults? Apparently, you know little of the history of the development of fiber optics for the tranmission of data under the oceans, or over very long distances. They had to come up with ways of producing so perfectly pure glass layers, capable of 100% total internal surface reflection, to avoid the data signals rapidly decaying over long distances. The account I heard on PBS's Innovation, about fiber optics, made it sound, like they didn't even know if what they wanted, would even be possible, and yet it proved to be.
So I suspect that it is perhaps more possible to produce such a "perfect" cable, than you seem to think. However, the latter concern of possible damage to the cable, seems a serious formidable obstacle though.
Also, what are the dangers of sudden cable failure? How susceptible is the cable to normal winds throughout the various layers of atmosphere? If such a long cable was to suddenly snap, it could travel at very high velocity, posing a serious threat to any space station or satellite nearby.
Also, I wonder if people are picturing the wrong design of a space elevator. Would it be simply a simple cable strung from a planetary anchor, to an orbiting, beyond geosynchronous orbit, pulling the cable taut? Could dangerous oscillations develop, yanking the satellite all around? Maybe wind pulls the satellite inward, and then it strays back out again, jerking to its maximum radius from the planet? Would the cable be "stretchy" enough, to absorb such oscillations? Anyway, how many people know that a conventional elevator has counterweights? I don't recall seeing the counterweights, in the video game elevator shafts I have entered? When the elevator car travels upwards, the counterweight travels downwards, so that the motor doesn't have to lift the entire weight of the elevator car. Only the amount by which the current elevator weight differs from the typical weight. This would save quite a lot of electricity over the expected lifetime of the elevator, and probably allow for the elevator motors to hoist the elevator up to higher floors faster, as the weight load is reduced, so the same amount of 480 volt? 3-phase? electricity can produce more speed, via lifting less weight. Now I don't know by how much, the counterweight is weighed. Can an elevator ever "fall up" should the brakes or motors hypothetically fail? Is the counterweight slightly heavier than the empty elevator car? So in a space elevator, where is the greater cost? Infrastructure, or energy usage? Could there be an elevator car traveling up, while another travels down as a counterweight? Would there be any counterweights, or would that just add too much weight to the system? Isn't it cheaper to produce energy on the ground, than to lift all that extra equipment or fuel? Does that mean additional cables, to lift the elevator up the main cable? A conventional diesel engine or generator, wouldn't work upon leaving the oxygenated atmosphere, unless it brings its own heavy oxygen canisters. Similar problem with fuel cells. And transferring electricity so far by wire, introduces that pesky copper wire "weight" problem, that the cable can't even support its own weight. Well unless the wire's weight is insignificant compared to the carbon nanotubes. Not to mention all the cummulative resistance, would just totally kill the current and power levels. If you plugged your leaf blower, into not just a 100-foot extension cord, but 10 100-foot extension cords, 1000 feet long, I imagine you wouldn't get much power, at only 125 volts. At the end of the run, under typical blower current, the voltage could dip to what? 60 volts or less? Or do the nanotubes carry electricity energy? What? With no heavy insulating layers? Maybe the energy for the elevators motors, can be carried by aiming lasers at a pickup on the elevator. But only a few miles up, and the target becomes impossible to hit? Maybe the answer to all that, is to keep the elevator motor on the ground, and use a separate hoist cable, that can be cranked down at the ground level, to at the satelite, go through some pulley, to pull a cable up, to lift the elevator. Remember you can't "push" a cable, only pull.
Compared to a rocket launch, a space elevator would be painfully slow. But a practical interest in space elevators would be, that the cost of transporting stuff into outer space, would be so much cheaper than by gas-guzzling rocket engines. I imagine quite a lot of unmanned loads could be sent up, to build space stations and such. Maybe to be offloaded by robots up in orbit. More stuff can be built, without the cost of rocket launches. More fuel can be delivered to rockets built up in orbit, to go farther out into outer space, without wasting the fuel escaping from earth's deep gravity well.
One reason why humans aren't doing all that much towards exploring or colonizing outer space, is that it's just too expensive for even humans to escape from earth's gravity well. A space elevator lowers this cost, making a whole host of things currently economically unfeasible, more feasible. Maybe there's not really much anywhere to go in outer space anyway, other than launching communication and weather satellites around earth? But will we ever find out, as long as the costs are so prohibitive? Technology seems to be changing so fast, that most of the satellites in orbit, are probably already woefully out-of-date. But they are so expensive to launch, that we have to keep them in service longer than we would otherwise like. This gives them even more time to develop faults or malfunction.
Of course, if somebody could invent a The Jetsons cartoon like "anti-gravity" beam to ride up upon, the elevator cable could be eliminated altogether. That would solve all kinds of problems. The biggest problem with getting into orbit, is the lack of any stairs to walk up upon. All that would be needed, is simply something solid to push against. Apparently, the Tower of Babel, rebellious attitude against God, people thinking they could just build a tower into the heavens, and find their own way to heaven, wasn't such a hot idea. Little did people know, had God not first scrambled the people's languages, the tower would have easily collapsed under its own weight, long before it could even extend as high as a mountain. What a huge boondoggle of a project!
Another way to launch into orbit, suggested by sci-fi I think, is some sort of space-airplane. Could it be possible to get going fast enough in an airplane to just fling outwards into outer space? Problem is, the planet's gravity well is so much deeper than the atmosphere's thickness. And gravity is a huge bear to beat by building up momentum, especially with air resistance to constrain it. Don't think so? Just try jumping up onto your home's rooftop. No matter how fast you think you can jump, one can't launch more than a few feet off the ground, without a major catapault or human cannon or something. Upon leaving the atmosphere, that may be great for cutting wind resistance for improving airplane fuel economy, but results in a very low earth orbit, not very useful for satelites and such? And then no atmosphere anymore, to "push" off of.