To Kanisatha - I talked about the distinction of what counted as being Faithless in the top paragraphs of my last post. Short of paying empty lipservice or actively renouncing the gods in general, the question of being Faithless does not come into the equation for us, in this game, or in general. Simply not following any particular deity does not make you 'Faithless'; that's what I was explaining.
It's as Piff describes; when Myrkul first created the wall, shortly after his ascension, it was designed in a deliberately cruel and punishing manner, that was tailored to reap as many souls as possible, regardless of what would be fair or just - thus, in its first incarnation, those who didn't have any knowledge or of even passing interaction with deities would be bound for the wall - even in this form, however, those who just made offerings or visited relevant shrines to their interests were still safe, as long as they did so in honesty - farmers who would pray to Chauntea for their harvest were fine, despite not being active worshippers of her. This was in the time of 3rd edition (and 3.5), functionally.
Many deities openly disliked the Wall, and felt it was unjust, but while Myrkul still held his folio it wasn't within the capacity of other deities to outright destroy it. At the time of the second sundering, however, many things were reordered, and many destroyed deities were reformed by Ao (Myrkul himself returned from being dead in this time - along with the other ascended mortal deities who had perished; Ao could not show favouritism with this action, so returning the good ascended meant returning the evil ones too, apparently). An opportunity was found, in this moment, to re-write many of the rules surrounding the Wall itself - it wasn't/couldn't be removed, but its rules could be remade, and they were. What this means is that now, in the age that correlates to 5th edition, the Wall of the Faithless actually doesn't get very many new souls, because the requirements to get left in the wall are much stricter than they were (as mentioned; actively renouncing the gods, or deceitfully paying empty lipservice are the main requirements).
Given erratas in more recent publications that make increasingly less mention of it, or remove mention of it altogether, there's a good chance that (in-universe explanation at least) it will fade from existence as fewer and fewer souls are fed to it, until it no longer exists.
Actually, I wasn't necessarily referring to Kelemvor's wall. I was referring to the fact that when a soul is faithless, such that when they get to Kelemvor's realm and they don't have a deity waiting there to claim their soul, they are vulnerable to certain deities effectively stealing or highjacking their soul right from under Kelemvor's nose. Llolth was famous for doing this, and so was Shar. They would capture these souls before they came under Kelemvor's control and forcibly take them to their realms as their prize. Kelemvor would angrily denounce this practise, but he was powerless to stop it.
But you still haven't addressed why players in BG3 can be faithless paladins but not faith-based paladins?