If you know that errors are dependent or if you know the distribution of the error, you can make an even better guess, but that certainly doesn't make averaging

If you know that errors are dependent or if you know the distribution of the error, you can make an even better guess, but that certainly doesn't make averaging "in general not a good idea." You're going to make assumptions whatever way you do it, e.g. using confirmation (two watches indicating the same time) to indicate truth assumes that error is fairly rare (out of 3 watches only 1 will be wrong at any given time) and that it's discontinuous rather than a smooth drift over time. No assumptions, no conclusions. Main point: more watches is always better, and three is not a magic number.