In Dante's Inferno, Dante uses the cross of his dead fiance, Beatrice, in order to absolve people. When you absolve souls, they are sent to heaven. At the end of the game, Dante uses the cross to absolve Satan, which means Dante just put Satan back in heaven.
Dante didn't absolve Lucifer, he just blasted him back into his prison. The ending does imply that part of Lucifer somehow piggybacked on Dante's cross-shaped sin tapestry and is now loose in Purgatory, but Lucifer isn't in Heaven just yet.
What about the Absolve and Punish options? Think about what those mean. Absolving would imply that you are sending them to Heaven, or at least Purgatory. That means that if you absolve one of the demons, you're giving a purely malevolent being a chance at eternal peace...while the countless souls in Hell that you don't absolve remain where they are. Then think about Punishment. These beings are already suffering terribly; how could you punish the damned? What are you doing to them that is even worse than the fate they've been given in hell?
Then consider that if Absolving souls (and demons) does free them from Hell, you have the power to save everyone from eternal misery—and most of them are there for petty crimes. Instead, you ignore 99.9% of them in your myopic quest to find Beatrice.
Fridge Brilliance kicks in: have you just noticed how many damned souls are there? releasing them all will require all eternity to say the least. And also the fact that if some of them are in hell there's a reason for this...
In which case, why would the game give you an opportunity to absolve Attila the Hun or Gessius Florus?
Dante recognized them and wanted to go over and personally punish/absolve them?
You can't really be absolved unless you want it and show regret. It seems every demon he absolves is a fallen angel that want to return to God's side.
As the babies are human souls the other entities we encounter must be human souls as well....
When Dante uses the Cross to Absolve the souls/demons, the symbolism is that the Grace of God/Jesus' sacrifice "burns" away all of what is bad/sinful in your soul before allowing you entry into Heaven. Hence the bright light. Most demons, however, are not simply fallen angels that you redeem. They're "constructs" of Lucifer's, made in mockery of "true" angels. So, what you're doing is actually burning them to ash, destroying them utterly, no chance of any afterlife.
Which brings us to the hugest case of Fridge Horror in the game: The next game will have you fighting God. Most of the souls in Hell that you can absolve seem to be there for petty crimes or honest mistakes, but they were given no chance of mercy or redemption. The only reason he cares about Dante and Beatrice is because of Lucifer's plan to marry her/use her to have Dante free him in order to return to heaven. As far as things show, God is just as evil as Lucifer.
Except you won't. More then likely you would have to fight Lucifer again since it's HIS plan to enter Heaven and God is the one who gives Dante a real change to reunite with Beatrice.
This may be in supplemental material, but I watched the Let's Play and don't have that. So, you have the Heretic and the Pagan. They look really similar, but the Heretic is immune to the cross. Why? The atoning death of the Messiah isn't where he erred.
There seems to be a lot of areas in Fraud that lead to nowhere, as short as they may be. Makes sense that realm of liars has dead ends and textures that look important without actually doing anything.
You visit the same areas in the Greed quite often. Could this be a metaphor for the cycle of earning/spending? Going through the first time, coming back with a new circumstance in effect and getting through it that time.
Whenever a Beast Tamer manages to climb on an Asterian Beast's back and try to wrest control away from him, he actually steals Dante's scythe for a brief while. If the Tamer succeeds (aka Dante fails the quick-time event), the demon will throw Dante off the beast along with the scythe. At first, this seems like an incredibly stupid move on the demon's part: why would he essentially give one of Dante's primary weapons back to him instead of keeping it or getting rid of it permanently? Until you realize that Lucifer needs Dante to break the Chains of Judecca for him as part of his Batman Gambit, chains that Dante can't break unless he's using the scythe. More than likely, Lucifer specifically ordered the Beast Tamers to give Dante a fighting chance and let him keep his weapons, as the end game of freedom from Hell is far more important to him than depriving Dante of one of his primary ways to defend himself.
Beatrice's brother Francesco died because he was executed for Dante's atrocities. This seems like it would be a Heroic Sacrifice, yet he is in Hell for it. This is because he helped a murderer go free, and the bible specifically mentions obstructing justice as something God detests.