To me it has nothing to do with "new cool kid" because it isn't a cool kid. It's hard to implement because of it's asynchronous nature. Websockets can also be used as "normal" connection. And because Tryton uses RPC, that can be transported by Websockets without a problem. But mostly there is a fallback to HTTP because not all browser support websockets.
By using websockets you lift the system out of the database like you want to do with the LISTEN / NOTIFY functions of PostgreSQL. Websockets gives you also the possibility to do some user-actions like sending notifications to a user from a module.
That's exactly what I'm thinking of! E.g. print a complex report or do a long-running operation like reconciliation or open the chart of accounts etc. You are then be able to give the user status updates during the process of collecting data or printing. I'm also thinking of voip integration, so when the phone starts ringing, the user gets a notification who it is. Eventually the client can already open a new tab with the caller details.
But maybe I'm a bit of there ....