During A World Without Superman, Batman intercepts a terrorist who wanted to blow up the funeral, and stated that in honor of his fallen friend, he was playing it by Superman's rules.
The Man of Steel AKA John Henry Irons is the only replacement who admits upfront he is NOT Superman; Rather, Superman saved his life and when he found out his inventions were being sold to gangsters, he created the Steel armor to fight crime in Superman's honor. Lois Lane notes later that, even though he's not Superman, he at least has plenty of Superman's spirit in him.
John saves a construction worker in what would have been a Heroic Sacrifice had Superman not been present. Supes tells John that it's easy for Superman to risk his own life because he has superpowers, but for someone without them, it's more impressive. When John tells Superman he owes Supes his life, Superman replies, "Then make it count for something!" Later, when Steel reveals he's John, Superman muses that John really did take his advice seriously.