There's no way in a land full of strange people like Totto Land that a 3rd eye would stand out so much it would lead to the level of shaming Pudding endured if it didn't have a deeper meaning. If there wasn't a more sinister reason. Oda doesn't like convenient backstories. They need to have bigger world implications.
I'm gunna need everyone who said it was a stupid & lazy writing choice to stfu already! Oda was 100 steps ahead of us & if we took the time to digest the text & analyze we all could've seen that choice for what it was: a narrative set up for a greater plot thread.
*Spoilers for chpt 1121 + some thoughts below
Poor girl is just the victim of years upon years of propaganda. The WG must've made sure any remaining people from these "special races" would not have an easy time hiding amongst socitey. They made sure to spread the idea of them being deplorable & disgusting so that any who escaped genocide (yes I'm using that word. Because I believe that's what it was.) would still suffer. All because those of the 3rd eye tribe have the ability to read poneglyphs. So in the same way the people of Ohara were considered too "dangerous" to live I'm sure the 3rd eye tribe went through something similar & it's history was just hidden or lost to time like so many other injustices in the One Piece world.
Imo this chapter is Oda confirming that Pudding is the last or one of the very last of her people still alive because the government has been actively trying to erase them from existence. Similar to Robin & King & Kuma & even fishman to an extent. Another layer to Pudding being a minority allegory.
SPEAKING OF KING! I think it's very purposeful of Oda to put this panel of him right next to Pudding. This implies that information about the 3rd eye tribe would be similarly coveted.
Is this why it seemed Big Mom kept Pudding's eye a relatively unknown secret? Why she kept her close & shown off like a rare jewel?? She knew she had a sought after "doll" & wanted to make sure no one else got ahold if it, but simultaneously wanted to brag about possessing it??
I mean she did get kidnapped as soon as her family's military forces were weakened. How many others with this sensitive information were waiting for an opportunity to strike? Plotting from the shadows like a thief?
"I'm not a doll mama" oh but it sure does seem like the world is determined to strip you of your agency & humanity just for the unfortunate fate of being born with an extra eye. How tragic.
The very last thing I want to say is more of a theory. One that doesn't have a lot of evidence for yet, but I think would work with the narrative themes Oda has built up through worldbuilding. Because if Pudding is one of the very last of her kind the question remains: Where tf did Big Mom find one to procreate with??
Could Big Mom have lucked out & bought a 3rd eye man at an auction? We know she's no stranger to the black market. We even see her men participating in Caesar's demonstration in Punk Hazard. Nor does she have any issues with viewing people as objects & things to possess.
We also know she likes "collecting" the strange & peculiar. Could she have been perusing the slave market for new & rare races? Is this perhaps why she felt the need to create a whole new 3rd eye person instead of just using Pudding's father?
Maybe he was too old. Maybe he was "damaged". Maybe he was sick & died before she could use him. Might also explain why Big Mom took the risk of only birthing 1 half blood child despite the gamble of genetics leaving the possibility for Pudding to not be able to unlock her awakening. She might've had no choice & now Pudding is her last hope so to speak. An asset she cannot afford to lose.
Ugh. All of this for me to ultimately say poor, poor Pudding. The more information we learn the more worried I get about her current situation. Can somebody fucking save her already? Free my girl Oda! Free. Her.
Finally, I just really need to put this out there:
Suck it Pudding/wci Island haters! She isn't going anywhere so get comfortable. I suspect there's more of her to come. Much, much more. mwahaha.