If no one believe that the dollar has any value, then it will not be accepted anywhere and lose all of its value overnight.
If it was merely based on belief the US (and other nation states) would have probably already collapsed entirely. It is force and violence that gives fiat money its perceived value. It does not matter what you believe as long as the government is able to force people to use it to pay them off or threaten them with violence if they don't accept dollars for settlements.
I don't think that people are forced to use fiat money, it is because that so far they have no other alternative and they never realized that there could be an alternative
The fiat money's value is maintained partly by existing consensus (unit of counting), partly by a balance between scarcity and availability through central bank's OMO
If fiat money can be acquired easily like toilet paper, then it will worth nothing; if people do not get fiat money as income (from top of the financial system: Government spending and bank lending), then it is no difference than a foreign currency or stock, not so many people will care about its value
Some belief affect people's life more than others. If dollar's purchase power dropped 50% in a week, people will lose their belief of fiat money, start to hoard physical goods and refuse to accept fiat money, thus accelerate dollar's fall. But if bitcoin's value dropped 50% in a week, most of the people don't care, since their income will not be affected
Things will get interesting when more and more people start to receive bitcoin as their income, but that might never happen at large scale due to ever rising exchange rate of bitcoin (people tends to spend inflative fiat instead of deflative bitcoin, they might even mortgage the coins and get a loan to spend)