Is the price the thing that would break faith in BTC, though?
For most - surely, but for those that understand that the price comes from the ideals that BTC has: I wouldn't think so..
Believe me, those who truly believe in Bitcoin as a "tool" to change the world are the small minority. The vast majority of people who join Bitcoin are only after the money. An event where all CEXs ban Bitcoin, would certainly cause panic. Even if we know the core Blockchain will remain untouched. With a huge price drop, no one will want to invest in Bitcoin. Especially if countries declare it illegal.
People will have to decide whenever they want to spend the rest of their lives in jail or continue enjoying their freedom (as in liberty). I'm sure many will choose the latter option, leaving Bitcoin behind in the dust. While BTC will survive, the number of supporters will be so small it would eventually "fail" (as a store of value, ofc). The odds of a worldwide ban are slim, so there's nothing to be concerned of.