@Mad:
No one is underselling Tamago and Pekoms. Just saying that it wouldn't make any kind of sense for them to be above Oven and Daifuku in either strength or pecking order of the Big Mom Pirates. They've literally been active pirates their entire lives.
What the government looks for is reputation. Assumed power. Buggy now has a public reputation as a guy who sailed with Gold Roger and is on equal standing with Shanks of the Yonko. They're probably well aware that he's not actually that strong, but the fact that people think he is should be enough to do the Shichibukai job. They're meant to destroy and intimidate other pirates. Same with Hancock. Everyone was aware of the reputation of the Kuja, so they offered her the Shichibukai position right away because people know just how strong they are and that their queen is going to become an ultra heavy hitter one day. Blackbeard took down the famous Fire Fist Ace. In front of an entire town's population. He didn't need a bounty, that feat alone can give reputation enough for Shichibukai status. Oda said that if the Shichibukai were active pirates, their frozen bounties would be much higher. See Jinbe. After he quit and joined the war, his bounty almost doubled. Shichibukai bounties are not good examples to use in any kind of discussion like this.
Because all he managed to do was make children with no emotions who aren't even that strong at the cost of his wife's life. And an army of clone jobbers. He didn't invent anything impressive like something that makes the Shichibukai obsolete. Or almost make giant children.
None of them put him down though. None of them actually fought him, they just tried to delay him/avoid his wrath. And every single time, he just got back up and asked for more. Bege sniped him and ran over him with a ship, and it just made him mad. Sanji kicked him and it just made him mad. Pound hit him with a stick and it just made him murder the guy.
Which is a level that a Yonko's heavy hitter should be above. That's the whole argument.
I don't know what you're talking about? If you're talking about Carrot, Daifuku never actually fought her. She spent her entire Super Saiyan time simply baiting him into destroying his own fleet. Very clever on her part, but hardly a show of her power against his. If she baited a drunk Kaido into blowing up Onigashima, you wouldn't say Carrot's power rivals Kaidos. Plus, Pekoms in his form got overwhelmed by a crowd of no name Big Mom foot soldiers.
The only difference between Pekom's and Tamago, and Daifuku and Oven, are that the latter of which are ministers of tottoland, as opposed to officers.
The germa are famed for their fighting prowess, don't really get that "they aren't even that strong" argument. Maybe they aren't commanders, but they still definitely heavy hitters.
For Oven, yeah, again, he has solid combat ability, however, although no one has never fought him down entirely, I think the ease many stronger combatants having getting around goes to show a difference in the level of strength between him and someone like Peros for example. Do you think Bege would have been able to run over someone like Peros, who had no difficulty stop Big Father in its tracks? Again, Oven is certainly a tough cookie, with particularly dangerous ability at sea and in close combat, but his by no means on the level of the sweet commanders or monsters like Peros in raw combat ability.
Your point about emperor heavy hitters is an interesting one. Oven is an emperor heavy hitter, but I think something that's been demonstrated multiple times already, is that members of the worst generation who join the crews of emperor's also tend to quickly become key figure's and heavy hitters in those crews. Drake became a flying six, one of the top six headliners of an emperor's crew(something I predict Hawkin's may also get), Bege became one of the most trusted and respected subordinates in the Big Mum pirate crew despite his short stay for his capabilities. This idea that heavy hitters in an emperors crew should be above that, with the exception of Peros, to me at least, is baseless.
For the Pekom's being overwhelmed by the crowd point, so was Sanji, and the point of that army, was that it didn't matter the individual who came through, they would be subjugated instantly, and that proved to be true on both fronts. Also, there were a shit ton of other ministers and other Big Mum siblings there. It wasn't exactly a collection of nobodies, it was a collection of dozens of heavy hitters of the Big Mum pirates, lead to by Oven.