There's nothing stopping browsers from tone mapping[1] those HDR images using your tone mapping preference.

[1]: https://en.wikipedia.org/wiki/Tone_mapping

What does that achieve? Isn't it simpler to just not support HDR than to support HDR but tone map away the HDR effect?

Anyway, which web browsers have a setting to tone map HDR images such that they look like SDR images? (And why should "don't physically hurt my eyes" be an opt-in setting anyway instead of just the default?)