I'm not sure by what authority you're judging what "should" happen, but by the rules prevalent in most cardrooms this isn't a requirement in ring games, limit or no-limit -- it's only a requirement in tournaments, although many players including me will do it NLHE ring games. Feel free to turn to
Robert's Rules if you're looking for a standard; I'm not sure what RR says on this matter.
Some sites are non-standard: Pacific doesn't show the all-in hands even in tournaments, which is pretty odd.