Hmm, I think you have a point, but I don't think it's that completely out of nowhere.
For this manga specifically, the thing about using tree branches against the proud ex-vassal is very convenient. I don't see Mahmut, who aside from his hawk, always seem to be a pretty straightforward to have the creativity to use tree branches as weapons. The pride is also just mentioned when the battle just started. Without those two, it would've been suicidal to fight it out in open field --- Same thing with the Chinese old man, hostage tent, and arrow's feather that almost started the war (though feather, I think, make sense since Mahmut is a falconer).
To have another fiction's example, I think it's kinda similar to how in Star Trek: Next generations they kinda always win in the end, whether it's during conversation between characters or the story's conflicts in general.
I don't have too much example about history, but I think during Japan's Sengoku Jidai, under Takeda Shingen, many new gold mines were opened. Combined that with the new knowledges they gain from the foreigners, they profit a lot and it becomes a pretty major factor on why the Takeda is as big as they are.
Plus, this one kinda is, bird shit. It's probably normal to not expect much from that.