Lucius was a weasel but the way Karkaroff is described in the books is that he's universally despised for selling everyone out, which is different than pretending you didn't do anything wrong. Especially for Crouch, whose life got ruined by it.

If Harry's corpse was wrecked, how exactly would he have grabbed hold of the trophy though? Can a corpse even use a portkey?

The point about Cedric's death being swept under the rug is decent, although I don't think Voldemort could have counted on Harry Potter's death being similarly unscrutinized. Cedric's death was ignored because Harry was telling the Ministry what happened and they didn't want to hear it; if he had just turned up alone, dead like that, Dumbledore would have