That sounds like an interesting way to provide more variety and player choice in running existing content, though as you say there will always be players who will calculate The One Fastest Way to get what they want.
Since the keystone (needed to use the system) is random every time you get one, it was mostly a case of sometimes you get a dungeon nobody really wants to run which makes it harder to pug for and/or all your friends hate that you get Halls of Valor every time.
Well, as long as they're using the hardest Garuda fight.
The true Dark Souls etc. etc.
Yeah I understand. Most MMO players aren't very open to changing that frame of mind either, so attempts to focus more on actual fun content vs. carrot-on-a-stick grinds will be met with fierce resistance. I can dream though.
Don't get me wrong, I like things that are for fun. What it ends up being is you'll find what's fun for someone isn't fun for someone else while
typically reward-oriented design has a broader appeal. In general, I'm a pretty big fan of don't design content for everyone but make sure everyone has content for them due to this; as long as everyone has that something that satisfies them, then I think that's better than hoping everyone likes everything enough. So what you describe as an offshoot to Aquapolis, Palace of the Dead, etc. seems like a perfectly reasonable thing that just adds "more to do" to the game.
Honestly, with the way more and more sources of tomes are added at this point, I really do hope for an eventual shift in designing the capped tomestone as more just a limit per week that you'll eventually hit since you're too busy having fun with literally every other thing possible in the game. That is, stop treating a capped tomestone as a reward and more just a fact of life.