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 only which involved threat to life. This is not what I understand the emergency funds is meant for. I see emergency fund as money kept for 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, buying something that becomes important which was not initially important, 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.
If you use the emergency fund to address the issues you mentioned, you may face losses. All these things you can spend from the reserve fund. Emergency fund should be used only when you/someone in your family is in doubt or you are in danger of losing everything. Especially emergency funds will be most needed in the medical field. The things you mentioned, helping a friend in danger, sudden arrival of a relative, buying essentials are not things that should be spent from the emergency fund. You can spend on all these things from reserve fund or floating fund, I think that would be best. After you spend from the emergency fund on any of these things, if you suddenly meet with an accident, the emergency fund can become a crisis. As a result, you will have no choice but to spend from your investment. Thus, you can harm your investment by spending unnecessarily from the emergency fund. So you don't spend from the emergency fund unless someone's life is in doubt.