The Wall Street elite aren't exactly known for being accommodating and playing by the rules that "normal" people play by. Their refusal to use forms of communication like email, texts, and chat is just another way for them to avoid doing things that average people have to do. These forms of communication are the norms and just because they're rich doesn't mean these Wall Street people should have to force their stone age tactics on others.
No, productivity won't be slowed by a small group of Wall Street elite refusing to say anything substantive in an email, text or chat. Wall Street bankers are successful due to productivity and speed. They are not going to allow something as small as this to interrupt business. They will find a way to work around it.
The refusal to exchange important information over email, text or chat is smart and overall saves time. Information is more likely to be compromised this way, therefore in the long run if the information is leaked it's actually counterproductive. So while the way to communicate may be fast, it can create damage that takes a long time to fix or that may not be damage controlled at all.
No, I do not believe refusing to say anything substantive in an email, text or chat is going to slow productivity. Our current generation has gotten too caught up in communicating online and not face to face. I believe this is a good practice that should be used more to help communication.