This would be the right time for arXiv to start accepting quantitative social science papers. Most papers at SSRN fall under that label. My guess is that most authors would happily move their papers from SSRN to arXiv in the blink of an eye.
However if SSRN is just a paper-hosting service, then everyone should move to the arXiv immediately.
The only issue I see with moving to arXiv right now is that currently arXiv only accepts papers on topics such as physics, math, and CS. For arXiv to be helpful to the SSRN crowd, it would need to have a few new categories (e.g., "quantitative social science", which could be split into subtopics mirroring the main topics in economics and management science journals).