Anzu being used as an overused plot device in some of these Puzzleshipping/Mobiumshipping stories grinds my gears.
You can’t think of any other conflict, so you use Anzu as a plot device/conflict of interest and you BUTCHER HER ENTIRE CHARACTER to suit your needs.
Think outside the box and stop using Anzu as your scapegoat, just because you can’t think of any conflicts that people have in relationships. Google is your friend—use it.
I don’t get people who can’t imagine any other conflict in a romantic relationship besides someone getting in the way and trying to break up the relationship either because they don’t approve or want someone in the relationship for themselves. Plus it’s so annoying that people almost always use Anzu for this role and completely derail her character for cheap drama.
Puzzleshipping is a ship I kind of like, but I rarely read fanfics for it and this is a big contributing factor. (However, puzzleshipping fanfics, hell pretty much every Yugioh fanfic regardless of pairing that is written by Higuchimon is good.) Similarly, I like Bumla/Vegeta from Dragon Ball Z, but the amount of people who need to bash Yamcha for that pairing is ridiculous and results in me only reading fics from a select few people.
I agree with your tags. I think even if puzzleshipping was a thing Anzu being a supportive friend would be more in-character. Even if Anzu was sad about it because she liked Atem or Yugi, or both, I think she would be okay with it if they people she cared about were happy.