So having bitcoin as a currency without any fiat wouldn't have changed the fate. No matter what currency system we have, this had to happen!
The reason you gave for financial crisis is succinct and correct. I disagree on the point that if Bitcoin had replaced Fiat and particularly replaced USD as the Reserve currency, even then the crisis would have taken the same shape.
The so called financial watchdogs of US were supposed to call out the malpractices while they were happening. They took the "too-big-to-fail" approach for heavyweight investment banks/ insurers and did not intervene timely. This approach is a direct result of the ability of these "watchdogs" to tide over any such screw-ups by simply printing more money. Quantitative Easing, they called it.
In a world where Bitcoin would be the reserve currency, such adventurism with people's money and savings would simply not be possible. Hence, the financial crisis and the ripple effect that Inflation due to pumping of more money has on the working class wouldn't have been so severe.