I think Adam let Blake run because he didn't want to show weakness in front of the White Fang. He seemed to be boss through intimidation and manipulation. Revealing Blake as a weak spot would lessen that.
Most of the organizations in RWBY don't seem "centralized". Printed communication has never been reliable apparently. The White Fang probably operates as "cells." So Adams cell (based in Mistral in seems) grew more extreme with him as leader. Sienna Khan was overall leader which advocated "violence in self defence." Adam could get away with what he was doing because he would claim "they shot first."
Blake could hide in Vale becaue odds are Mistral and Atlas didn't share a wanted picture. Even if they did Torchwick had the cops overwhelmed. Where did Ozpin talk to Blake in V2 though? It doesn't seem she was arrested but still debriefed.
The S.D.C. brand on Adams face in V6 was probably supposed to show that he had valid reasons for being as extreme as he was.
The talk about Yang semblance was about her semblance being a hammer so every problem was a nail. Yang lost to Neo because Neo could run circles around Yang. Then Yang lost to Adam because she charged in with her semblance instead of thinking.
I think living on Remnant makes people stoic by nature and Yang had a more resilient personality to begin with.
-Pretty much all organizations in RWBY are set up in whatever way they're needed at the time. The White Fang in the first several seasons came off as a rogue group that recently turned violent after Adam overthrew the previous leadership. Infamous but still a relatively small group. Then later on they decided to make them a worldwide organization just to have Adam kill the leader and usurp her anyway which was utterly pointless. Sienna Khan as a character didn't so much as get hinted until Volume 4 which is when much of the story decides to throw out all of the previous seasons and change things to be completely different. Blake suffers from that problem as well in the same season when her previous backstory which implied Blake was either an orphan or didn't have her parents in the picture so she had a hard life was retconned into Blake being a Faunus princess who lived in a mansion on a tropical island and didn't really experience any discrimination. It makes her a massive hypocrite and makes her come off as petty and whiny more than anything.
Blake didn't bother to change her name, outfit, or weapons when she went to Beacon, so either there was no proper record of her as being part of the White Fang or literally everyone in the world is too dumb to realize that Blake Belladonna at Beacon is the same Blake Belladonna in the White Fang. And considering Mile's capacity for thinking ahead I can guarantee the actual explanation was never thought of in the first place. This is a problem with the lack of worldbuilding in the early seasons but as the writer of the show since Volume 3 Miles is obligated to think things through. The least he could do is throw in a line trying to explain it but there's nothing of the sort.
The SDC brand was a laughable last minute attempt to give Adam any kind of character after they already threw his character out. And I guess to try to make the face reveal seem like it's meaningful after spending 6 years building up to it. It was really last minute and shallow especially after they made Adam into a complete joke in Volume 5.
-Yang was chastised for using her Semblance at all, not for her poor tactics. Yang did use her Semblance in the Vytal tournament but so what? Everyone else used their Semblances too. Is it bad she used her Semblance to win against Flynt Coal when he used his Semblance to almost win? Or against Mercury when he used what I assumed was his Semblance to bombard her with a crap ton of shots (until Miles decided to be an idiot again and say Semblances can be taken probably cause he discovered All For One in MHA). Yang didn't use her Semblance against Neo she lost simply because Neo outwitted her and played to Yang's weaknesses. In a world full of man eating monsters that are supposed to be what they're training to fight against who cares if she uses it against human opponents in a tournament that's supposed to be for fun? Yang used her Semblance sparingly in the first couple Volumes as a last resort in a fight. When she fought Junior she used it to end the fight, and when she fought Roman in the mech she used her Semblance to take it down after he smashed her through a concrete pillar. I can understand if the goal was to say Yang needed to think more level headed in fights and be more flexible, but it was handled in a really clumsy way.
And this didn't come off as Yang being resilient. This came off as her losing every bit of her personality. She was boring and obnoxious. I've seen people go "She's traumatized!" as an excuse for her storyline being boring and badly written but it comes off as her being mopey and lazy. The world is in danger and she just sits around doing nothing. There's not a whole lot of time in the season to develop Yang's trauma and it's mostly ignored anyway and just a few episodes in she puts on the robot arm so all that mopey stuff was inconsequential filler. If they wanted her to get back in the action quicker just have Yang be dead set on revenge against Adam. That would have been more in character.
Nevermind that his name is literally Adam and that his symbol is a wilting rose, one of the main motifs associated with the Beast- nah, we gotta retcon him into Gaston and throw out what could have been a really interesting morally grey character and turn him into a screaming abusive incel to pander to the part of the fandom that's so toxic it makes the goddamn Elephant's Foot jealous!
I'm still frustrated over how hard they shat the bed with him, man. He was one of my favorite characters and post V3 they just butchered him.
Yeah I forgot to mention the rose theme! Adam literally has a rose embroidered on his coat. You'd have to be a compete shill to not notice that Adam is based on the Beast.
When I started watching RWBY I expected that Adam would be more of an ideological opponent to Blake and their conflict would be something akin to Gray Fox and Solid Snake in the early Metal Gear games where they ended up on different sides of the conflict due to their personal views. Blake tries for peaceful resolution but Adam thinks that violence is the only way to get Faunus rights. You know something interesting like that. Instead when Adam shows up in Volume 3 they completely warp his character into being a psycho stalker ex despite him being called Blake's mentor by Monty. Miles just wanted the crazy ex angle cause he's incapable of writing an interesting villain.