The alternative is the website operator who wants to save on bandwidth instead adopts JXL or WEBP or what have you and ... the end user with old software still can't open it.

It's a dichotomy. Either the provider accommodates users with older software or not. The file extension or internal headers don't change that reality.

Another example, new versions of PDF can adopt all the bells and whistles in the world but I will still be saving anything intended to be long lived as 1/a which means I don't get to use any of those features.