Looking at the DOM in isolation, its pretty quick. The primary reason web apps are slow is because the business logic is typically un-optimized.

I've encountered a web app that persisted its state by stringifying it and putting it into localStorage with every UI change. The resulting string was ~5MB and took 200-300ms each time (freezing the UI) on my tablet.

I've encountered an app that used an in-house built chart library using jquery and D3. For each chart rendered it created a 50MB array of x-axis labels that wasn't cleaned up when the chart was destroyed.

The reasons for why these inefficiencies exist is another topic. But there's nothing stopping someone from creating a complex web application that's performant.