My 2 cents...
I agree with pretty much everything that's been said. I think the biggest problem is sometimes there isn't any instruction for a lot of musicians in church. Some musicians really just find their way and like someone said earlier they learn a lot of licks and cool tricks and can't wait to try them out and to some it sounds busy. I think we fall short though if we don't at least try to raise the "busy" musician's awareness to his playing. Meaning, if you stop playing with someone, I think its unfair if you don't tell them why. I'm a huge advocate of communication because you never know someone's heart or their musical/spiritual maturity...I remember when I first started, like a lot of people, I was kicked off organs/keyboards/pianos and a lot of times no one ever told me why and I would actually know the song and could play. I think we owe a duty to other musicians to tell them what they are doing wrong and how their ministry may or may not be effective when we see error...
Also, a lot of times, I think musician's that become tasteful were probably busy at some point in time because they may still be "honing their sound" and then as they matured, as was said earlier, they then become more tasteful. I guess what I'm saying is a busy musician isn't always trying to show off...but may be trying to find themselves musically...