They had an opportunity to rail at the system and cast themselves as the vanguard and champion of their users's rights. They were doing everything they could to cover the collateral obligations, but the big bad clearing houses and various market makers were dead set at dousing a bit of water on the fire. Instead they kept to the line, "There is no liquidity problem", which was a bald faced lie to protect against a run and/or loss of faith as you point out.
If there was any lesson to take from GME/meme stocks, "lack of faith" due to poor fundamentals is not a problem haha. Users would have LOVED Robinhood more if they perceived them as helping them fight "the power". But they chose not to and anecdotally any of my friends that were caught up cooled considerably on Robinhood, I don't know a single of my dozen or so acquaintances still using it fearing that Robinhood will fail them when it is critical.