I happened to be reading the section on precision for binomial confidence intervals in BBR and was following up on references. The text recommends the Wilson method for a frequentist CI and links to a Wikipedia article. Following up on those citations lead me to a critique of the arcsine transformation I discussed above.
These authors recommend the logistic model for discrete data, or a linear transform for continuous data.
This seems reasonable to me for individual studies, but there might still be a justifiable, educational use of the arcsine transformation in the context of meta-analysis.