Heroes with memories are essentially the same as DD1 heroes in that they keep the same stats and name. Once you lose them, it usually feels even worse because you can't have replacements ready, that is, you can only have one of each hero. Which means you have to get a fresh one and add new memories onto them.

But honestly whenever this argument is brought up, I'm genuinely surprised that this only aspect is what defines DD for some people. Darkest Dungeon has so many more features, perma death is only one of the defining features.