Bitcoin will always be dependent on fiat. Only if people were to completely accept bitcoin would fiat be rendered useless.
Yeah, and I don't see it happening in near future as the market cap of fiat is huge as compared bitcoin, so bitcoin would be surely dependent on fiat in future too.
There are chances if everything goes digital then we can expect that people would use more bitcoins as a payment method in compare to fiat, but that doesn't mean fiat will simply disappear.
That's true even if everything goes digital we would still find many users that would be dependent on fiat and they would continue to use fiat as they are using it since a long period of time.