How can meta-research improve statistical research/practice?

Meta-research has spurred two opposing perspectives on science: one treats individual studies and study series as two separate publication types (e.g., in Ioannidis' 2005 paper 'Why Most Published Research Findings Are False') and one treats individual studies as part of a series that needs to be informed by that series (e.g., in the Chalmers et al. 2014 paper 'How to increase value and reduce waste when research priorities are set'). These perspectives decide what statistical methods are valid, both at the individual-study level and at the meta-analysis level. Could meta-research also inform which perspective is most appropriate and improve the corresponding statistical research and practice?