BTC is a future currency and a renowned digital asset whereas USD is a mainstream currency regulated by a centralized authority; primarily both must be run simultaneously as it will maintain the balance though BTC has a huge future prospect than any other digital asset.
I fully agree with you, one without the other will not exist. At least until bitcoin is fully part of our lives. But when it happens, and for bitcoin will be in the store to buy bread, then we will see the battle of the titans for survival!