It is all about efficiency. The alison engine that is used in lots of helicopters would have a hard time producing enough thrust to get it off the ground without a rotor. The way a lot of turboprops work is by directing the exhaust from the gas turbine over a power turbine that turns a shaft which goes into a gearbox and then turns the prop. I beleive the major reason turboprops are not built to go fast is due to the compresibilty problems of propellors at high speed (they become very poor at producing thrust). Modern airline engines such as the RR trent are not just jet engines pushing out thrust from their exhaust to make the plane go forwards. The big fan stuck on the front (the one you can see when you look at the front of an engine) acts like a propellor and is the component that produces most of the thrust at low altitudes. As the aircraft climbs the thrust percentage switches to most of it comming from the exhaust of the gas turbine rather than the fan. That is why they are called turbofan engines. It is a compromise between a pure jet which is good at high altitudes and a turboprop which is good at low altitudes. Turboprops do not need to be able to produce thrust from the gas turbine because they never go high or fast enough. They usually stay where a propellor is more efficient. Pure jets at low altitude are very inefficient. Jet fighters use them however because they need to go faster than you could with a prop although lots of them now have low bypass turbofan engines. Airliners mainly have high bypass turbofan engines which means there is a lot of air that bypasses the gas turbine. Look it up on google they will have pictures and give a better explination.
http://www.grc.nasa.gov/WWW/K-12/airplane/aturbp.html
http://www.grc.nasa.gov/WWW/K-12/airplane/aturbf.html