Isn’t the in-story and fandom comparison of the BWB with Robin Hood and the backstory-only Kingswood Brothehood fundamentally flawed? Unlike Robin Hood of legend and the KB, thge BWB were originally legal officers of the Crown who got screwed over a coup (analogous to the Resistance of World War II) rather than dedicated outlaws. They don’t do much theft or highway robbery. I always thought Jaime’s refusal to understand that, as a mark of how flawed his judgment was.

Depends on the version of the Robin Hood story you’re using, but a lot of the later ones have Robin Hood as fighting in the name of Robert Lionheart as the true King of England, so there’s a resonance there. Also, the BWB do expropriate Sandor’s gold and ransom Arya, which is pretty Robin Hood-esque. 

As for the Kingswood Brotherhood, the resonance is even stronger:

• Wenda = Maid Marion.

• Big Belly Ben = Little Jon.

• Fletcher Dick = Robin as archer.

• Simon Toyne = Robin as disinherited nobleman.

• Smiling Knight = Will Scarlet. 

Also, the Kingswood Brotherhood were very much into robbery, kidnapping, and fair maidens, and had the support of the smallfolk for defending them against perceived royal injustice. And had songs written about them:

No man’s gold was from them,

nor any maiden’s hand.

Oh, the brothers of the Kingswood,

that fearsome outlaw band.