As many of the other commenters here mentioned, it is much easier and lower work load for the pilot to fly forward than hover. It also takes more power from the engine to hover than it does to fly forward, and this largely has to do with the effects mentioned above about having to pull air from above the rotor to below. That also saves me quite a bit of gas. One thing I do not see mentioned here is that it is also significantly safer to fly forward than hover, in the sense that there is a much larger margin for error in forward flight than there is in a hover, and I'm going to make an effort to explain.
Helicopters, in the case of engine failure, can auto-rotate. This basically means you're "gliding" the helicopter (it works like those sticks with a propeller on them that you spin between your hands and they fly a little bit). Auto-rotating while moving forward is much easier to do, and is much more gentle, than auto-rotating in a hover. If I auto-rotate in a hover, I first have to convert some altitude into moving forward, and once I'm doing that, I can "glide" towards the ground. When I get near the ground, I convert the forward speed I now have into the rotor, so I basically come to a stop and a gentle landing. What does this mean, in practice? It means that if I'm moving forward, I can auto-rotate at any altitude. I can auto-rotate anywhere from 20ft to 15000ft altitude. If I'm in a hover and have to auto-rotate, I will probably need somewhere between 200-500 feet of altitude to successfully auto-rotate and land safely. When I'm flying, I'm comfortable hovering very near the ground (1-30ft) and I'm comfortable hovering at 500ft+. I'm far less comfortable (from a safety perspective) hovering at 250ft than I am at 1000ft.
I tend to think of the rotor spinning as a "battery". If the rotor stops spinning, I have no energy, and I will fall out of the sky. The rotor is constantly using energy to keep me flying, and that use of the rotor's energy will slow it down. I can add more energy into the rotor by using the engine, but I can also convert both forward movement and altitude into spinning the rotor. If I lose the engine, I will start to descend to keep the rotor spinning until I get near the ground. Now there's no free lunch, so what I can't do is trade my altitude for rotor speed, and then use exactly the same energy to trade my rotor speed into stopping my fall. It has friction, etc., and so I will hit the ground VERY hard if I do that. What I can do though, is be moving forward too! So now I'm moving forward, and I'm trading altitude for rotor speed, which basically means I'm falling slowly (descending). When I get near the ground, I can slow the helicopter's forward movement, and convert the forward energy into rotor speed too! This means I can stop moving forward, and as a result, have a very soft landing. That is why I can't auto-rotate from a hover easily. First, I have to convert some of my altitude into moving forward, and only then slow down my descent as I get near the ground. Then I convert that forward movement into making my landing nice and gentle. Converting that altitude into forward movement will take me about 200-400ft, which is why helicopter pilots don't like hovering at low altitudes.