So per the request of GoldenVenus, writing my version of a theory on the giant straw hat being stored by Im in the Tenryuubito vaults. Just like One Piece, I believe there are treasures of monetary value, but that's a separate theory.
Im is already an oversized human, so with the scaling, this mugiwara boushi is HUGE. Even Elbaf Giants might not be able to wear this hat comfortably. There is a commonly repeated theme that is providing a pretty clear answer though: the MASSIVE giants. Parts of this are genetically/environmentally altered like Big Moms dream of giant children and Shiki's dream of an army of giant animals respectively. The theme continues with the recent revelation of massive giants with Kaidou's Numbers.
Going to go on a bit of a tangent. Hacchi (hachi is 8 in Japanese, so we probably have Numbers from 1-10 to match Jack, Queen, and King), is a goofy and comedic-effect overly, oversized human. I am biased to think we will have legitimate powerhouse fighters among the Numbers. Maybe they are ranked by strength with 10 being the weakest and 1 the strongest (matches the Ace being the best card in many games). Sure Hacchi has high destructive power, but Luffy can do more than that in Gear Second. I've had theories in the past on scary giants would be if they have soru (top tier strength with top tier speed/mobility). This is essentially what Kaidou and Big Mom are; Giants that have high rankings for every combat capability. Hacchi appears to be stupid and slow, but the higher ranking Numbers being that size because of an awakened zoan means they could be even stronger than King (they are bigger than King, so if they have the same speed but greater strength/destructive power then they are higher ranking by power but not by title). This fits because it seems like crew members in the 100 Beast crew are not allowed to openly fight for titles (a decision has to go down the chain of command so Kaidou or main execs have to give the OK). Logistically, if they are crazy party animals, having the weaker but more responsible Jack/Queen/King is the right call by Kaidou.
To continue the tangent, the high ranking Numbers could be start of the people stronger than Luffy but still below Yonkou/admiral level. They can defend against a Yonkou/admiral for a short time, but would get overwhelmed since there is still a big power gap in all aspects (7 days for Aokiji vs. Akainu). The point is that even this tier of fighter is world changing. Yonkou/admiral levels of combat capabilities might not have existed 800 years ago. There is not record of when haki was discovered. Without haki, physical combat capabilities could rule the world (outside of the Ancient Kingdom's technology).
And this is where the theory gets interesting. Since the Ancient Kingdom was open to anyone from any species and we know they interbred to have the genetic variety, it makes sense that there are the genetic cross-overs and normal/natural mutations resulting in the freak occurrence of a massive powerhouse (just like Big Mom is a child of normal parents). Imagine if no one in the world is at Luffy's current power level. And suddenly we introduce someone at this theoretical top tier Numbers level of power. If they had the brains, which is the norm for gifted people, they immediately climb higher and higher in the Ancient Kingdom. Most people are good in the Ancient Kingdom, so the high success rate and the extent of helping people out would lead to this person being the "king" of the Ancient Kingdom. Their crown: this giant mugiwara boushi. We know any mugiwara boushi carries symbolism through the importance to Roger, Shanks, and Luffy. Makes sense for this to go all the way back to Roger's/Luffy's distant relatives in the Ancient Kingdom.
So just like Luffy's treasure, the giant mugiwara boushi is more of a symbol. Just an expansion of the current theme. Going to keep it simple because I think this fits the best. Of course Oda could always introduce new stuff to make it a weapon.
I'll probably come back to add a picture or two. Any thoughts? We're always open to other theories! This one is completely open-ended, so no wrong answer since we have no background context on it.