Only if a dev has screwed up. Most simple sites are fine. You have to push the DOM quite hard for the browser to be the bottleneck. I've worked on apps that have DOM trees with 60,000+ nodes that remain under 16ms (because very few were actually changing at any given time..)

games with vastly more complex sound, network, physics, UI and whatever else systems render frames in < 8ms at 4k

The Servo project is bringing a lot of what makes game UIs fast to browsers. It's a massive shame that it's not a Mozilla/Firefox backed idea any more but it's still going. Hopefully it'll get a bit more mainstream one day.