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 that it isn't a must or compulsory to set aside emergency funds before you can start accumulating bitcon because since there's no existing bitcoin portfolio you can possibly protect the emergency funds with if unexpected problem should happen, i think it's unwise for someone to build up his or her emergency funds first before getting started with accumulating Bitcoin. Instead of building up your emergency funds and later accumulate bitcoin, if you can figure out your 3 months expenses, it is better you get started with accumulating or investing in Bitcoin, and after some months into your accumulation process, you can start building up your emergency funds as you are accumulating bitcon should in case unexpected problem happens, you can see where to depend and solve the problem without you selling part of your Bitcoin to get it solved.