What are the arguments in support of retrial for the greater offence under section 1157 of the Criminal Code?

In summary, in section 1157 cases the arguments in favor of allowing retrial for the greater offense after reversal of conviction for the lesser offense are: (1) when the jury fails to specify the degree of offense in its guilty verdict it deprives the state of the right to a full and fair opportunity to convict the defendant of the offense of which he is guilty; (2) the defendant's interest in finality of judgment is not applicable because a new trial is the natural result of his successful appeal; (3) the holding of Green v. United States is not applicable to convictions under section 1157 because the jury did not choose to convict the defendant of the lesser degree of the offense and may, in fact, have been prevented from doing so.