I liked the feature of VI that showed who you've won with, and which conditions you've won with - an enhancement of the Hall of Fame that's been around since at least III.
I might like the "enhanced version of Steam achievements" aspect of the paths by itself. That sort of thing can encourage playing with different styles, or it can encourage all players to play towards the same objectives if it is too specific.
But I don't like the memento unlock system as described. One, the "easier over time" effect, which also affects multiplayer if enabled - in all likelihood, at least some of the later mementos will make things easier, even if an effort is made to balance them. Two, the likely high number of times that one must play each leader to unlock them all. Civ games aren't short, I'm not going to play every leader multiple times. Which means that in most games I won't be able to choose the mementos that correspond to the leader I am playing.
But more fundamentally, I don't see how this improves the core game. Being able to choose between a couple of options for your leader's traits, sure, that gives some strategic customization. But shouldn't the focus be on the in-game mechanics, not some sort of meta-game? Playing a Civ game in order to unlock a different Memento for the next Civ game seems silly.
It could certainly be worse. There are far too many games with microtransactions or lootboxes, and thank goodness Civ isn't going to be one of those games. But it still concerns me that this is deemed important enough to be the focus of the seventh dev diary, when there seemed to be a lot more depth that could have been covered after the first six.
