Maybe some day.
Maybe some day.
Related: there is also a CSS property coming which allows sites to control which page content should be clamped to standard range or not. Worst case you can just add an * !important override in your Safari->Preferences->Advanced->Style Sheet if nobody else considers it problematic but you still wanted to clamp things (in Safari, otherwise you can just disable HDR).
I don't think it'll be problematic though because a site can already choose to show you images a lot more bothersome than a bright light (I say this as I type on a 1600 nit HDR monitor) already and that's not a particularly common problem to worry about either. Same for videos, which already HDR support in browsers.
But this is hardly true. There are some complicated heuristics (like Chrome's "Media Engagement Index") but many websites can and do autoplay video and audio. And browser policies are even more relaxed for playing audio on user events (like clicking).