That's how all fiat currencies work. For example, to use your words:

People think dollars have value because they're accepted by other people because other people think they have value.

You accept your paycheck in whatever currency you accept it in and believe it has value because you have faith that other people will accept that currency for whatever goods and services you want. It all works as long as everyone believes the currency will keep having value in the future. Bitcoins are no different. As long as a group of people believe they have value in the future, and will be accepted as payment for goods and services, they will continue to have value.