I feel so bad about this because I don't like being negative, but for the life of me I don't know why so many people love Guitar Hero III so much. I thought the boss battle gimmick was garbage, the charting was all over the place, the visual effects were outlandish in a way that vastly messed with the rhythm and timing of the notes (so much so that they had to widen the allowance on timing just to counterbalance it), and everything was overcharted as hell.
It's an exercise in style over substance. a great track list from a popularity aspect but nowhere near as fun to play. I got introduced to way more songs and bands from Guitar HEro 1/2 and the Rock Band series than this. And yes, there's a distinct correlation between developers HArmonix (the team that made GH1, GH2, 80's, and the rock band franchise) and my personal tastes.
Buh, this is one of those games that I know most people only like because it was the one that had the widest appeal, but there's a dedicated group of music lovers that feel it was definitely a step down. Rock Band did it better.
Because it's fun.
And one way it was made more fun for a lot of people is exactly in widening the timing for hitting notes. No one's gonna disagree with you that it was ridiculously wide in GH3, you could hit notes like half a second early or late. I suppose many things were overcharted, but because hitting notes was so easy, it made you feel better than you probably were. And everyone probably felt that way, really. That's just fun.
Also, the songs were awesome. Whether previous games had more or less awesome songs is personal taste, GH3 still had a killer soundtrack.
I agree with you that Rock Band did it better, but maybe Rock Band's existence is the exact reason why I never looked down on GH3. The Guitar Hero series definitely got wackier from that point on, prioritizing dumb fun over precision, and it was easy to embrace that because if you ever wanted that precise gameplay again, Rock Band was right there.