Symphony by accident

My example of music was admittedly an extreme case, intended for emphasis. But the point is that you have randomness that is fed into a filter. In our normal way of talking, we don't use "accident" when there is a directional filter.

It seems unlikely to me that there exists a way to count actual fixated mutations and classify them as to whether it was due to selection or drift, so I don't think we could know either way whether what you're claiming is true. Maybe one of the biologists will chime in.

We do know that advantageous alleles will be driven toward fixation more rapidly than neutral alleles, but as fixation approaches the effects of drift become more prominent and can actually interfere with fixation. Apparently, in sexual populations recessive advantageous alleles can actually have a better chance of fixation than dominate advantageous alleles simply because of the effects of drift. See Natural Selection, Genetic Drift, and Gene Flow Do Not Act in Isolation in Natural Populations.

Well, again, the topic was the eye, and whether Richard Dawkins thinks it happened "by accident". Clearly he thinks that the filter of selection is strong enough to produce the eye; consequently, he does not think that the eye is accidental.

I think you must be operating under the impression that advantageous mutations that do not reach fixation are somehow lost, which is definitely not the case. It also appears possible that you think fixation is some kind of holy grail for alleles, and that alleles that do not attain fixation do not have a significant impact on a population, also definitely not the case.