Notification incrementing is not purely client-side state though. It's triggered by an event coming from a server. Eg let's say you're on a product page and you click 'Add to Cart'. You want the cart icon's counter badge on the top right corner of the page to increment. With eg htmx when you click 'Add to Cart' we send a request to the server, it updates the cart state in the backend, then sends an HTML fragment response that updates the necessary parts of the page, including the cart item counter badge.

In my experience it's just exceedingly rare to require this. My insurance company website has a notification thing, and it's actually static. You need to refresh the page, and considering how few and far between notifications are, and how common refreshes are, it works fine.

There's an entire domain of apps where you truly need a front-end. Any desktop-like application. Like Google Sheets, or Figma. Where the user feedback loop is incredibly tight for most operations.