You are absolutely right that it is important to have an emergency fund so that we do not have to sell Bitcoin at a difficult moment and of course we must have an emergency fund before investing. There are most new investors who enter the investment but do not make their financial plan and emergency fund before entering.
Yes having an emergency fund is important when investing in Bitcoin but it's not a must to have it first before getting started into accumulating Bitcoin, what is most important at first is having your discretionary income this is what you use in accumulating Bitcoin then on the process you can think of setting your emergency fund gradually by then you have already been accumulating Bitcoin with your discretionary income either using the DCA strategy and HODL.
I agree with you, it is definitely worthless to think of an emergency fund before investing. One should start investing first and then build an emergency fund to regularize that investment. If one does not start investing to build an emergency fund, then that emergency fund has no value. If an investor follows DCA and at the same time builds an emergency fund for 3-4 months, then at the same time his emergency fund will be built along with his investment. As a result, on the one hand, he can increase the amount deposited by DCA of Bitcoin and on the other hand, he will also build an emergency fund.
when you invest early definitely it has benefits, especially with strategies like DCA where consistency matters i think having at least a small emergency fund it is very important, even just 1 or 2 months of expenses you can create a safety net so that you will not be forced to pull out your investment early if unexpected happens. building both side by side it will be of good help, than depending on someone's financial situation.