The reason I don't chase mementos is because I can only have one at a time, and I don't necessarily want to go through all my crafted weapons and decide which one looks best with the memento at any given time. Even if it's just 3-5, being able to stack a few of the same memento would be very nice, and would make me much more likely to grind them out.
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I need this. I often forget to use my Trials momento every week and just lose the one I get for first flawless.