All the websites I maintain do what you suggest, as does Free Republic. But sadly, nearly all websites nowadays look like they were designed by people whose only skill is in designing fixed-format wall posters. The original purpose of HTML was to share information between people with very different hardware and even handicaps like poor vision. Nearly all modern web developers have forgotten this. I think one of the problems is that nowadays anyone who knows how to use a word processor thinks they can be a web developer; and things like portability to different viewing devices, accessibility, etc. have become lost arts.
I have to use an outdated Russian version of opera just to read FR on my iPhone.
Yep. The last time I shopped for a smart phone, none of the sales people for any of them could show me anything with a browser that would reformat websites to fit the screen. They were all like index-card-sized PDF readers. I suggested to one salesman (Android) that we try downloading "Opera Mini" and that worked.
Pale Moon (based on Firefox) also gives a great rendition of FR on my Android phone.