You are right I will love to add that Emergency funds should not be tampered with or used for your needs, and being replaced back. Emergency funds is always there as stand by at all the time and not to be spent only when a real emergency happens that needs to be taken care of immediately if not it will worsen the situation of things that will lead to more damage . For instance, if you lost your job, or the roof of your house was pulled of by storm. You can rely on your emergency funds for the mean time till you get another job, so that you don't sell your bitcoin to survive during when you don't have a job. Your income should be divided, whereby you have set aside for your needs.
If a real emergency happens, and you use the funds like the example, I gave above, when you get a new job, you can then replace/build back your emergency funds. This is why we should have a good size of emergency funds, so that whatever emergency that happens, it can sustain us. It is also good because that is what will also consider how aggressive we will be when accumulating bitcoin through DCA in a particular time.
Seems we have a little difference in our ways of viewing the emergency funds, and you are obviously viewing it from the negative aspect which involved threat to life. This is not what I understand the emergency funds is meant for. I see emergency fun unplanned events not covered in personal planning of expenditure. Emergency funds can include unplanned visit of a relative, support to a friend that is in desperate need of help, indeed it could come in different ways and not only when threat to life is involved. Loss of job which is in other words loss of the source of income is a different ball game because in such situation, the emergency funds may not be able to cover your needs such as rent, feeding, medical, etc and still allow you continue to DCA as you were doing when you had the job. So this will require a different plan all together until you secure another source of income.
I guess it will matter depends on your needs and as long as you didn't use it on things that unwanted like buying your unnecessary need using your emergency funds then everything is fine. But for me I usually separate some money intended for emergency cases like medical needs,losing my job and I need some funds to cover my expenses on the days when I'm seeking for new job or if I experience a heavy income loss and need some money to get up on this unfortunate situation.
So people should always think that having a emergency fund is important and they should not always think about their investment since its like their safety net when there's unfortunate changes that they didn't imagine will happen to them.