I studiously avoided making a normative statement that economics should take over this role. Any personal preferences I have here are separate from my beliefs about what I predict to happen. :-)

I ~agree with you about the quality of econ papers. In some cases, I see the quantitative facility of econ papers as being better than similar studies executed by e.g. sociologists. But in some cases, flashy quant skills are used to distract from more fundamental issues.

Assuming my prediction that social science research shifts to econ comes to pass, I think the natural pressure will be to drag econ's present quality bar downward.