The "plenty of great websites" were developed long time ago. Having a degree of visual consistency of layout across different browsers was not possible then according to standards.
The content will not be lost. The tags will result in valid elements but the rendering may vary. This has always been a thing to be expected, since legacy elements (pre HTML5) never had uniform rendering and contained quirks.
Should the current/new standard have support for ambiguously rendered quirky elements? Is it even a standard then?
After HTML5 the end result will definitely be the same on most (if not all) layout engines. The standardization as a process requires non-conforming legacy to be dropped.
The content will not be lost. The tags will result in valid elements but the rendering may vary. This has always been a thing to be expected, since legacy elements (pre HTML5) never had uniform rendering and contained quirks.
Should the current/new standard have support for ambiguously rendered quirky elements? Is it even a standard then?
After HTML5 the end result will definitely be the same on most (if not all) layout engines. The standardization as a process requires non-conforming legacy to be dropped.