Matt,
Firstly, the Apache is not a piece of crap. The A model is the most capable attack helicopter in the world, hands down. As for Army doctrine, I totally agree with you on that. It has taken the Army 30 years to get back to the tactics and doctrine developed in Vietnam and away from the myopic "tank killer" role that the Apache was originally intended for.
The Apaches in ODS, OEF and OIF maintained close to 90% mission readiness rates throughout the campaigns and were in the thick of the fight for a majority of the combat for all three.
As for those helicopters that have been shot down, there have been more AH-1Ws shot down than there have been Apaches in all three operations. In ODS, one Apache from the 101st was shot down. In OEF, none have been shot down, although several were unflyable after landing at their FARPs during Operation Anaconda. And in OIF, three have been shot down (one from the 1-101st and two from the 1-227th, one each tour), all after taking an incredible amount of punishment. The Apache remains the safest helicopter to fly in combat, and only ONE aircrew has ever been killed in combat while flying the AH-64.
I'm not getting down on the Cobra. I love the bird and wish the Army would bring it back in the armed scout role. But for pure attack and close air support, the Apache is the way to go.