A task being on the critical path is neither desirable nor undesirable; it simply is. Every task might make a crucial contribution to the overall masterpiece, "each musician a vital component." If it's not, then why do it? The analogy misses my point.

What's undesirable is a critical-path task that is delayed, thereby delaying the entire effort, as you pointed out. If the first violinist arrives late for the concert, that's a problem. So if I'm the first violinist, I'm going to ensure that I'm not late, that I'm not holding up the performance.

Methinks your problem is with my title, or perhaps with my philosophy of trying not to be the bottleneck, rather than with the discussion of the critical path. That's fine; you're welcome to whatever critical-path philosophy you like. I simply like to recognize when I'm facing an activity that has the potential to hold up the whole project. I complete such activities as expeditiously as possible.