Yes, fiat will eventually go away in its current form. But I've been reading that (and thinking it) for over a decade now. It's going to take time. Longer than you or I would like.
The crypto market still needs time to mature. This will include bear markets. During bear markets, even the best crypto assets (the ones that rise to the top as you accurately describe) will be undervalued. That value could be higher than where we are now for some, but also much lower for others.
Diversifying is great, but that should also mean keeping some USD ready for when your favorite crypto is cheap. That's just my friendly advice.