It is worth noting that the Emergency fund isn't as flexible as every other backup funds, such as the reserve or float funds. Tampering your emergency fund or using it to serve the purpose of the discretionary income would only mean one thing, which is endangering your Bitcoin portfolio. The Emergency Fund should in fact be treated as a rigid cushion as it is the ultimate safety net for your Bitcoin investment.
Now imagine a situation where you hit a potential DIP in the market and it's just so attractive that you feel you can't miss buying on that DIP, and maybe in the absence of a reserve fund or discretionary fund, you decide to opt for using your Emergency fund to buy the DIP (leaving your Investment defenceless and vulnerable), with intentions of replenishing it in the coming weeks, and then just after the buy, an unexpected emergency suddenly pops up. Now, there's no emergency fund in place, no reserve or float fund, you're left with nothing but your Bitcoin investment, what do you think would happen in such a case if not to dip into your investment to sort out that emergency...
I understand your point mate, it will a foolish decision for any investor to use all his emergency funds of at least three months of his monthly expenses to buy bitcoin at once because of a drastic dip that he does not want to miss because at the end if he is hit with real emergency like you said, he might lose his total bitcoin portfolio to such emergency.
However, in a situation where the investors is expecting his weekly income in two days time and he sees a drastic dip, he can take out only the amount of money that he has planned to DCA with on that week from his discretionary income and buy bitcoin so that, he would not miss the dip. When he gets paid in two days time, he can replace the money which he took from his discretionary income.