Bitcoin does not need the dollar, right now the most powerful currency is the dollar and that is why every currency is compared to it, when bitcoin takes that spot then every currency will be compared to bitcoin instead.
Agree. Bitcoin being decentralized in nature, is well against government's ideals, making it quite difficult to replace the dollar anytime soon. As the pioneer cryptocurrency is not capable of handling all of the world's transactions, the dollar will have quite an advantage in this regard for many years to come.
However, if cryptocurrencies like Bitcoin become stronger and fiat currencies become weaker, at some point, the former will have the possibility of replacing the most well-known currencies in the world like the US Dollar and the Euro. But given the fact, that governments are exploring into blockchain technology, fiat currencies will survive for the long term once the switch is made, leading them towards the same level as cryptocurrencies.
Nevertheless, while Bitcoin may be far from replacing the dollar soon, it could stand alongside it, that can be used as an alternative payment system in the time of need. Just my thoughts