That makes about as much sense as "not using server-side scripting."
Personally, I have had great experiences building purely client-side rendered apps, with DB and other APIs exposed to the client via REST. I now consider HTML generation on the server (with separate rendering logic from the client) to be an antipattern -- done right, the same rendering logic should be usable on the client and server, and can prevent whole classes of bugs and frustration.
Of course you have a choice. You can build a new service and place it in front of the other service. For example using Node.js. But I agree that a SPA is often the right way to go.