...There is no need building an emergency funds to protect your bitcoin investment when you don't have any bitcoin because you have nothing to protect...
I think this your statement is very wrong. Emergency funds is very important for anyone whether they are investing in bitcoin or not. Since emergency situation like paying of hospital bills, car repairs , accident etc, this are situation that we don't have control over hence there is need to have an emergency funds since since such emergency situation doesn't just occur to bitcoin investors alone. Having an emergency funds before investing in bitcoin will help in protect your assets.
You're the one mixing stuffs up for yourself. If you're not investing into Bitcoin you can have those discretionary funds as cash reserves or savings or in other forms that tailors to your description.
In Bitcoin investment the emergency fund is specially dedicated to handle real emergencies that may arise which ordinary you're not prepared for and this is to prevent your portfolio from being seen as the feedback plan and tampered at a time that you don't choose. It's important you start your Bitcoin investment first before building out your emergency fund because you'll be wasting time that you should've used to get a decent stash of Bitcoin for yourself building out only your emergency fund while you could've done that side by side with your consistent investment into Bitcoin. It's a win win situation when you build out your emergency funds alongside your Bitcoin investment until it can service at least 3 months worth of your expenses.