Why is the latency so high?
The way a satellite stays in orbit, without using any type of engine or rocket to correct its orbit, is to gain a balance between gravity and centrifugal force. The closer to earth, the greater the gravity pulling the bird toward earth. The faster it moves, the greater the force pulling it away from the earth. It turns out that there is a spot, about 22,300 miles above the equator, where the speed an object must travel to gain equilibrium against gravity is exactly the same as the speed the earth is turning. By placing a satellite in this spot, its relative position above the earth stays constant. Satellites used for broadband internet and TV must stay in one place in the sky so that you can point your dish in one spot and get the signal. The only other alternative would be to have a constellation of satellites in a lower orbit, that would rise and fall like the sun and stars. There would need to be enough of these flying that there was always one overhead, which requires a lot of satellites, a lot of infrastructure ,and therefore a lot of money.

In the case of a two-way satellite system, when you request something by clicking on a link, or any other way, that message travels 44,600 miles just to get to the NOC. The stuff coming back to you must travel the reverse route, so the round trip is 89,200 miles. The speed of light is 186,000 miles per second in a VACUUM,slower through the atmosphere. But even if you assumed 186,000 mps then the total time taken in space travel is about 480ms. Given the atmosphere problem, it is actually more like 500ms. Add to that the terrestrial internet latency, which should be about 100ms. Also you can add delays through transponders, gateways, proxies, etc.
Software and protocols can reduce the effect of latency for certain applications, but they can't change the physics...the latency remains. For instance, by increasing the number of simultaneous TCP connections, WEB pages can load faster after they get started, but they will always take the same amount of time to get started. Better yet, by replacing the protocol between the NOC and the user from TCP/IP - which doesn't handle high latency well at all - to another protocol designed for long fat pipes, even more could be done to reduce the effects of high latency. No doubt, that is the future of these systems. But still, there will be a delay of somewhere around 625+ms between any interactive activities. The latency of one-way systems is obviously less, with the space travel being cut in half.