Yeah I'm also trying to figure this out. I'm not seeing a clear pro or anti move here, and I'm also trying to figure out what the point of only listing a house via email or such ... not sure what is playing out here.
The rest would be mitigated by your realtor/agent handling silly requests... I'm not sure I buy into that theory.
They aren't "silly" requests, and the realtor has a legal obligation to present offers to clients, so I'm not sure how you want your hypothetical screening to work.