I should state that "A Roguelike with a twist" does not a "Roguelite" make.
Since well... Pokémon Mystery Dungeon to me is absolutely a roguelike without question... and actually one of the best ones ever created.
Though I don't like the term "Roguelite" anyhow... While I am against weakening a definition until it becomes meaningless, I am also against making the definition too strict so that innovation can never occur...
Roguelites should be relegated to games that have strong roguelike elements without ever really crossing into the genre.
All that is important to me for a Roguelike is if the Core Gameplay is in tact.
Heck none of the stuff I found amazing in Nethack (the logical design point on certain things) ever crossed over to other games.
significant carryover between games (emphasis on significant; yes, many roguelikes have ghosts, but that's very different from Phantom Eden's, uh, Phantom Eden) is the big Thing That Makes This Game Arguably Not A Roguelike
Here is kind of the thing... Ignoring Pokémon Mystery Dungeon and a few other roguelikes that actually featured this... Why is "No carryover" a necessary element? Because Nethack didn't have it?