Are you just knowing that an emergency fund is for real-life situation all this while, there is something i want you understand, before you can buy or invest in Bitcoin you must have a discretionary income and this discretionary income is fund if you lose will not affect you much and which Bitcoin is beyond you lose all your money that you investment, since you have a steady cashflow you will always have plans for yourself outside Bitcoin investments, and which the same thing you should do when it comes to Bitcoin investments to avoid touching your holding incase if unforeseen circumstances occur you can make use of the emergency which no one is praying for it to happen but we just needed to plan ahead of us since no one can predict the future.
Steady income => steady investment process => good chances that you are going to be okay if the trouble eventually hits.It doesn't matter if you have a steady income or not, if you don't prepare for the days you will be in lack, or in serious health issues that might compel you to temper with your Bitcoin holdings, in a situation like that, if you don't have emergency funds in place to sort it out, your Bitcoin holdings will not survive on the longer run because emergency situation is inevitable on the longer run.
I really disagree with you with this your statement that it doesn't matter if you have a steady income or not, and if you don't prepare for the days you will be in lack, or in serious, there is something i will love you to understand in Bitcoin investments and both outside here that you don't know, if you don't have a steady income how do you sort out your discretionary income or more of having an emergency fund, so brotherly you should know that for you to succeed in Bitcoin investments and also outside here you should have steady income that can help you sort out your discretionary income and emergency fund and also help you have a prepared planing on how to go about your investments.
Even if you plan to sale a plot of land that can give revenue as wise man you still use the money to start up a business that can be given you a steady cashflow and still you sort out your discretionary income from there, so that you can still invest and be alright.