Then everybody will wonder why and want to use them. The ban would not work anyway and it will make the government look really bad. There is a country in South America that has banned it but I dont remember which onw.
Not really instead it is the other way around. Remember Governement have all the power and trust of the majority of its people. So if the government labeled BTC as illegal and banned it, those who are holding BTC and trasacting with it will really look bad. Because these people will go underground transaction in order to use their BTC.
Yes its a game of trust and the one who has maximum trust, wins the game. People trust fiat currency because the government trusts it and again the government is peoples organization so while bring it to the micro level, one trust a $10 currency note because the other one do the same and they mutually have the unwritten agreement that they agree, a $10 note has the value of $10. Same about bitcoin, if all bitcoin users believe that bitcoin is worth $10,000 then everyone will have to believe it.
We do believe with bitcoin as well as it's price, but it's based on fiat so we can say that without fiat bitcoin will not exist. The government is the highest authorities in this world, we elected them and they make laws and we fully because we trust them. You are right, it's a game of trust, without it this world will be in chaos. In the end, if they decide to ban bitcoins, we have to respect and trust them.