Oooohhhh I agree so much with all of this. If I may also add my two cents...
Something that I have heard a lot of people with these theories say is that Charlie needs to be taught a lesson that some people are not capable of redemption.
This is something I come across as well, and it ties in neatly with a post I recently saw here on Tumblr stating that 'some of you have never watched The Good Place and it shows'. The message of that show, which I also truly believe will prove to be a core message in Hazbin Hotel, is that anyone can be redeemed. Exactly as Charlie says multiple times throughout the show, for example in response to Vox in 2x3 when he asks her if she thinks even he could be redeemed.
It's not that some people cannot be redeemed, it's that some people do not want to be and will not put in the effort to try.
Keeping in mind that unless angelic steel is involved, the sinners in Hazbin's Hell have eternity ahead of them. Eternity. Just take a look at Zestial: that guy's been in Hell for centuries!
Are some people seriously going to say that if a person, no matter how cruel they may have been in life, were to dedicate decades or even centuries to bettering themselves, that still wouldn't be enough to redeem themselves? Say a person killed 10 people in life. This is horrible, absolutely horrible, and yes they would deserve damnation for their crimes. But if, once in Hell, they were to genuinely try and change, dedicate themselves instead to helping others, to saving lives if possible, whatever is within their power to put good out into the world, and they make a consistent effort to be a different, better person for years, would that still not be enough for them to find redemption?
The concept of redemption in our human, mortal perspective is a tough one sometimes, I understand. In life, we don't have eternity to right our wrongs. Depending on what crimes a person commits and what hurt they cause, there comes a point where a human lifespan is not long enough to make up for the damage they've done, no matter how much one may try. You can't wash away a lifetime of hurting others by donating away every penny you have and doing genuine good in volunteer work or whatever at the end of your life. Sometimes the damage is too great to be repaired in your lifetime (in the very worst cases at least).
But in Hazbin Hotel, as in The Good Place, these human souls are not bound by time. They get eternity to try, to stumble, to fall, to get up and to try again. They get eternity to learn from their mistakes, to acknowledge the damage they've caused, to try and be better tomorrow than they were today (props if you get this reference)
Under circumstances like these, Charlie is not naΓ―ve for believing that anyone can be redeemed (even if some never will be). I'd rather say it's naΓ―ve and shortsighted to believe that people cannot be redeemed when offered eternity to try.
The ones who will never find redemption, their problem is not a matter of being incapable of change, it's that they're not willing to try (for whatever reason this may be; some might genuinely enjoy cruelty and evil, some might believe themselves incapable of change or undeserving of redemption, or a multitude of other reasons)
Charlie doesn't need to be proven wrong. Charlie is entirely correct. And her staunch belief that people are always, always capable of change if they just try is perhaps the most mature belief in the show. Her methods need work, but her belief is solid, and she does not need to be proven wrong.
(In regards to Alastor, too, I agree entirely with OP here btw; narrative redemption is also a concept that exists, and it is not (necessarily) synonymous to ascending to Heaven in Hazbin Hotel)