Is a loss of trust in USD necessary for the success and mainstream adoption of Bitcoin? Considering that Bitcoin will succeed if it gets to become a widely adopted store of value and means of payment, current fiat currencies' role would be taken by BTC and the value of those fiat currencies will be much lower than today's, if BTC succeeded.. 

And if that USD crises ends up happening, wouldn't a collapse of global economy probably come next?

Am I missing something? I don't think I like my conclusions as much as I'd like BTC to actually success...
There is not black and white answer here I guess, but here is my logic.

Let's say that trust is a proxy of security and stability and satisfaction is a proxy of liquidity, usability etc.
If we look at the extremes: if people had 100% trust in the USD, then they are less likely to look elsewhere for alternatives (holding everything else constant). Therefore less trust in the USD is more likely to increase BTC adoption and hence value.
However an improved usability, liquidity and other functionalities may be good enough reasons to increase BTC adoption as well.
Therefore, we can conclude that a loss of trust in not necessary, but it will help.