I don't think JPMorgan needed any government intervention. Goldman didn't directly, but if AIG had gone under so would they. (To be fair, so would the entire financial system.) But in the end, both of them got help.
Citadel didn't. It wasn't in that club. It is not now. If Citadel failed tomorrow, it would make headlines for a week, and then we'd move on.
Meaning 'too big to fail' applies to hedge funds now just like investment banks. Ala LTCM
LTCM wasn't making markets and it was done in by leveraged bets on Russian bonds.
The term you are looking for is systemically important financial institution (SIFI) [1]. BlackRock, with $9 trillion under management, is a SIFI. Citadel, with under $40 billion, is not.
[1] https://en.wikipedia.org/wiki/Systemically_important_financi...
JPM received $25B in CPP funds on October 28, 2008 and repaid it on June 9, 2009.
Aside from CPP, any bank that had assets affected by TARP purchases -- or by the potential that follow-on programs could affect those assets -- had its balance sheet ballasted in one way or another by government intervention.
All of the banks that survived will say they didn't "need" government intervention, for the same reason that they don't like to borrow from the discount window: it looks desperate to take help from the government. But technically both of those banks received an injection of liquidity via TARP.
They had the, "we didn't avoid the mortgage mess, we just made more money on shorts than we lost" and "we are very well positioned" emails that became evidence in the Senate investigation into the GFC. The ones are the namesake for the book/movie The Big Short.