Typical web image quality is like it is partly because of lack of support. It’s literally more difficult to show a static HDR photo than a whole video!
HDR should not be "typical web" anything. It's insane that websites are allowed to override my system brightness setting through HDR media. There's so much stuff out there that literally hurts my eyes if I've set my brightness such that pure white (SDR FFFFFF) is a comfortable light level.
I want JXL in web browsers, but without HDR support.
PNG supports HDR with up to 16 bits per channel, see https://www.w3.org/TR/png-3/ and the cICP, mDCV and cLLI chunks.