Think of all the powerful and useful Devil Fruits as well as their users. Which are abilities that the Blackbeard pirates should realistically know about and be capable of hunting down?
Here's a set of criteria:
1) The BB Pirates have to know this person exists and what power they posses. For example, they can't hunt down Enel's Goro Goro because they don't know who Enel is, that he has such a powerful DF, and that he's currently on the moon.
2) Going after this person should not drag the BB Pirates into the possibility of a war with a great power. Killing Kizaru for his Pika Pika would undoubtedly bring the full wrath of the Marines against the BB Pirates, even their own man Kuzan might choose to backstab them over this. Maybe Burgess would be such a fool, but the more capable hunters like Shiryu and BB would wait for the right circumstances.
3) It cannot be a high difficulty hunt the BB pirates might not find worth the effort. Not simply in terms of power level. Marco would be a high difficulty hunt because he regenerates all the damage he's taken instantly and can fly away over the seas with his pheonix wings should his life be in danger. Blackbeard could certainly defeat him in a 1v1, but Marco would not fall for it after the Payback War and is therefore hard to capture and kill.
I'll start off with Burgess and his missed opportunities in Dresrossa.
Here's a set of criteria:
1) The BB Pirates have to know this person exists and what power they posses. For example, they can't hunt down Enel's Goro Goro because they don't know who Enel is, that he has such a powerful DF, and that he's currently on the moon.
2) Going after this person should not drag the BB Pirates into the possibility of a war with a great power. Killing Kizaru for his Pika Pika would undoubtedly bring the full wrath of the Marines against the BB Pirates, even their own man Kuzan might choose to backstab them over this. Maybe Burgess would be such a fool, but the more capable hunters like Shiryu and BB would wait for the right circumstances.
3) It cannot be a high difficulty hunt the BB pirates might not find worth the effort. Not simply in terms of power level. Marco would be a high difficulty hunt because he regenerates all the damage he's taken instantly and can fly away over the seas with his pheonix wings should his life be in danger. Blackbeard could certainly defeat him in a 1v1, but Marco would not fall for it after the Payback War and is therefore hard to capture and kill.
I'll start off with Burgess and his missed opportunities in Dresrossa.
Pica's Ishi Ishi.
Burgess should have obtained the Ishi Ishi no Mi, no doubts about it. A giant golem terramorphing all of Dressrosa's landscape, that should have made it abundantly clear to Burgess that is a damn good DF with scary potential. He knows who Pica is because he looks like the golem. Zoro sliced and defeated this man before Luffy even used Gear 4th. All Burgess had to do was walk over to Pica's body and do his thing or capture the body alive and hid it somewhere.
Burgess should have obtained the Ishi Ishi no Mi, no doubts about it. A giant golem terramorphing all of Dressrosa's landscape, that should have made it abundantly clear to Burgess that is a damn good DF with scary potential. He knows who Pica is because he looks like the golem. Zoro sliced and defeated this man before Luffy even used Gear 4th. All Burgess had to do was walk over to Pica's body and do his thing or capture the body alive and hid it somewhere.
Sugar's Hobi Hobi
The little girl that transformed hundreds of civilians, pirates, animals, government officials, etc into weak obedient weak toys that everyone forgot about. Maybe even Big Mom and Kaido would lose to such a power. Perhaps Burgess didn't grasp the full details of this ability as all of Dressrosa changed back, but for sure witnessing just one or two of its effects should have made him think this was an obscene, disgusting DF. Burgess knew the Doflamingo family was behind this given their reaction at the toys turning back. Maybe he didn't know it was Sugar with this power, but all he had to do was beat up and interrogate a Donquixote family member. Sugar was knocked out cold and inside the castle, Burgess was also inside the castle looking for DFs. A huge missed opportunity for the luchador.
The little girl that transformed hundreds of civilians, pirates, animals, government officials, etc into weak obedient weak toys that everyone forgot about. Maybe even Big Mom and Kaido would lose to such a power. Perhaps Burgess didn't grasp the full details of this ability as all of Dressrosa changed back, but for sure witnessing just one or two of its effects should have made him think this was an obscene, disgusting DF. Burgess knew the Doflamingo family was behind this given their reaction at the toys turning back. Maybe he didn't know it was Sugar with this power, but all he had to do was beat up and interrogate a Donquixote family member. Sugar was knocked out cold and inside the castle, Burgess was also inside the castle looking for DFs. A huge missed opportunity for the luchador.
Barto's Bari Bari
This is technically a high difficulty hunt for a meathead like Burgess, but due to the events of Dressrosa I find it doable. Burgess was in the colosseum to see this barrier block King's Punch. He was in the same ring with Bartolmeo in the final round. Bartolomeo packs nowhere near the raw power of Sabo and just relies on his barrier. That should have been everything Burgess needed to see to target this OP DF. Of course, Burgess himself would never get past Barto's barriers. If like a good hunter, Burgess actually tracked his prey then he would seen multiple opportunities before Luffy ran out of G4 and he ran over there. Bartolomeo uses his barriers to make stairs for Luffy and his body as a human shield against Gladius, big wide open opportunity to kill him. Barto suffers heavy damage blown away by Gladius, he's vulnerable again. Barto uses the barrier to help some civilians and heavily injured allies push the bird cage, Burgess can take them all out from behind. The Kurozomi family of trickers loves this power, the BB pirates would have too.
This is technically a high difficulty hunt for a meathead like Burgess, but due to the events of Dressrosa I find it doable. Burgess was in the colosseum to see this barrier block King's Punch. He was in the same ring with Bartolmeo in the final round. Bartolomeo packs nowhere near the raw power of Sabo and just relies on his barrier. That should have been everything Burgess needed to see to target this OP DF. Of course, Burgess himself would never get past Barto's barriers. If like a good hunter, Burgess actually tracked his prey then he would seen multiple opportunities before Luffy ran out of G4 and he ran over there. Bartolomeo uses his barriers to make stairs for Luffy and his body as a human shield against Gladius, big wide open opportunity to kill him. Barto suffers heavy damage blown away by Gladius, he's vulnerable again. Barto uses the barrier to help some civilians and heavily injured allies push the bird cage, Burgess can take them all out from behind. The Kurozomi family of trickers loves this power, the BB pirates would have too.