In meta-analyses of proportion studies, funnel plots were found to be an inaccurate method of assessing publication bias.

By J. Hunter, A. Saratzis, A. Sutton, Rebecca H Boucher, R. Sayers, M. Bown. Journal of Clinical Epidemiology, 2014

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Co-infections in people with COVID-19: a systematic review and meta-analysis (2020, neutral): “11 plots and statistical tests potentially yielding misleading results.(66) Although publication bias may cause inflated estimates in meta-analyses of studies of treatment effect, this is an unlikely scenario in the context of studies reporting the proportion of patients with co-infections in COVID-”
Methodological guidance for systematic reviews of observational epidemiological studies reporting prevalence and cumulative incidence data (2015, methodology): “However, one study found that conventional funnel plots appear inaccurate when there are either low or high proportion outcomes.(22) As such, funnel plots ‘using sample size as”
Visual Inference for the Funnel Plot in Meta-Analysis (2019, background): “Indeed, empirical research suggests that subjective interpretations of whether publication bias is present or absent, based on mere visual funnel plot inspection, often times are wrong (Hunter et al., 2014; Simmonds, 2015; Tang & Liu, 2000; Terrin, Schmid, & Lau, 2005).”