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.
Only listing a house to buyers that can actually afford it and not having to waste time dealing people who need to get a mortgage with the bank who ultimately rejects the buyer. These aren't low end, low demand properties we're talking about. It makes it a "who you know" market, especially one where you don't want eg tabloids theorizing why you're selling the house. Eg if Beyonce was selling one of her mansions. The pool of qualified buyers for one of those it's a relatively short list, and the list of people she'd actually want to sell to is shorter still. in that kind of market, you don't need or want to publicly put it up for sale.
Literally being in the tabloids is a minor concern, yes, but hopefully you are able to generalize beyond that.
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.
Indeed, I recently was asked to sign an NDA to view an off market home; the seller was (apparently) a local business owner and didn’t want folks thinking the business might close — in many industries confidence in long term staying power is critical.