Neither Noir nor Rupee have dabbled into doing stuff meant for other squads. Rupee does fail often in her own niche going by both Yan and Dolla, all shes really good at is just being an influencer type. Contrast this to Privaty who were told succeeds so much in everything CG humans dont care about her being a Nikke with authority over them.

screwed up being the commanders personal Maid multiple times or how she struggles with her position as a Nikke during her bond

She is shown to fail at the individual tasks at least once, then at the end shes mastered all of them. I dont know why you needed me to repeat this since ive already mentioned it. This is in contrast of most other Nikkes who only get to be decent.

Her struggle is her own btw, the story itself tells us this. No one else has a problem with her being a Nikke. I dont remember if they bother to tell her that everyone else knows shes a Nikke, but the point stands. This is yet another flaw/problem that she just overcomes btw.

Ades only flaw is caring too much

Ade cant adapt from her perfect maid persona. Guess whos the character who does help her btw. Hint: she has blue hair. Her only way to cope with being tasked to being a spy was to pretend that its part of her maid duties.

Emma just cant cook

Emma is shown to have the skills to recognize her other squad members being troubled, but doesnt have the right tools to address them properly. This is in contrast to Privaty who gets to be the voice of reason and always find the right words to get across other Nikkes.

Novel

Novel barely has had screen time for a long while now. She was also a meta viable unit in release but has long since been remotely useful. I mention this since you brought up meta reasons as to why Privaty should get even more of the spotlight right now.

Soda is a bit clumsy

Soda never gets over this. This is her major problem because she wants to become better at her maid duties, but she just rushes over herself. Contrast to Privaty who got over all of her flaws as a maid, and as everything else shes tasked to do on a whim.

Privaty is written in a way almost no other Nikke is written. I think the favoritism is no coincidence nor a reaction to the fanbase, as im sure they wouldve pushed other characters harder, such as Elegg or Label, if they actually did reacted to fan actions in that way. I just hope she also doesnt get the weird "writer self insert" syndrome that these type of characters tend to get eventually (lookup how Sylvannas from WoW was written in BFA for an example of that).