Ok a few examples of how stats can add depth to the game (and note that when I say stats, what I basically mean is numbers as used to define your character; not necessarily just the labels that are visible to the player):
- If I make two characters, and both of them walk into the same ancient dungeon and find a really old book written in some kind of ancient language, one of those characters might possess the knowledge to read it, while to the other character it's just nonsense. How does the game determine whether a character has the knowledge? Through numbers / stats.
- If I go and hit an NPC, leave town for a week, then return and speak to the same NPC, will they remember and take a hostile attitude towards me? Again, stats are necessary to determine this.
- If I make several characters, and all of them need to break into the same castle, each one might try and enter in a different way. One might bribe the guard, one might try and climb the wall, one might overpower the guard and take his key, one might sneak in through a back entrance, etc. Stats determine what your character can and can't do, what their strengths and weaknesses are, etc. Which in turn has an impact on their actions.
In an ideal RPG, i'd want everything the character can possibly do to be determined by stats. Every single thing about them should be uniquely defined to make them as complex as possible... and to make their interactions with the gameworld as complex as possible.
I think you have used poor examples for the use of stats.
Your first one is about knowledge which isn't about stats (least not purely), its about what a person/character may have or haven't learned, and how good a memory they have, and the opportunity to put it to use.
The second is partly about memory (on the part of the NPC), and there's other things involved like did you go back disguised or not, or wearing different clothes ect, are you using illusion spells. Stats can help, but knowledge, memory, and use of spells and/or skills on both for both parties, can over come useing stats.
And your third example, whilst a bit, theres more to a character than stats alone (the same can be said about skills). stats can play a part, but not by themselves, theres more to making a character than stats, skills are just as important, how the character acts, that he/she does or doesn't do.
Stats have their uses, but the game has to allow the player to use them. Stats aren't always necessary, and also can be pointless if not utilized.
On a personal note, I do think stats like strength ect getting removed is a shame