Arya Would Have Survived In King's Landing
The claim that Arya wouldn’t have survived if she had been in her sister’s situation is an overly repeated idea that can’t be supported by canon. In fact, the theory goes against canon since it requires misinterpreting Arya’s character and completely misunderstanding the political situation in King’s Landing.
To sum it up quickly for TL;DR purposes:
- The Lannisters needed hostages as leverage against their enemies. If they killed those hostages, they would lose any leverage they might have and put Jaime at risk.
- Arya survived in Harrenhal where she was forced to serve her enemies and conform her behavior to protect herself from additional abuse and murder. She did this without the protection of being a valuable hostage. If she could do that, she could have done the same in King’s Landing.
This post is long and full of canon.