Well said, I believe there is no necessity why one will want to build an emergency funds firstly when he can invest with any little capital, and also build emergency funds along aside his Bitcoin investment. As you earlier said, we have no control over natural occurrences, same way we can't comprehend how far our emergency funds will go while investing or any unforeseen events happen.
There one thing we should understand, Emergency funds aren't fixed funds, rather are suppose to be liquid ( by that I mean continually growing it), not a fixed amount you think, in essence it is pointless and a waste of time to not invest when you can, you simply control your risk, leverage on your sources of income and build your reserves overtime.
I see the point you are trying to make and i am convinced, if a person can invest and build emergency fund all together then it is the best thing to do but then majority of people are struggling to make ends meet and are barely able to invest so building both emergency funds and investing at the same can be difficult for some. Building emergency fund will only delay ones investment reducing the possibility of buying at a lower price and that’s why DCA strategy have been of great benefit making it possible to invest at intervals and also creating the possibility to build emergency funds as well. It’s just about knowing how to balance the two and not be too aggressive with either leaving aside the other.
If you read the last post by JJG, you will see that he has explained clearly on how to go about building your bitcoin investment and your emergency funds simultaneously without leaving one aside. I don't want to repeat what he said.
you are the person who only has 2-4 weeks worth of back up funds at the time that you invest into bitcoin, then maybe you can figure out some kind of a formula to build both of those, and so for example, first get the bitcoin investment amount up to 2 weeks of your expenses, and then try to simultaneously build both.. and don't let your emergency fund drop absent an actual emergency (such as loss of cashflow or illness or something like that), and if you do have to use any of it to build it back up to get it back up at least to the size of your bitcoin investment, and sure maybe by the time you build both your bitcoin investment and your emergency fund up to 3 months then you might start to be able to build your bitcoin at a pace that is faster than your emergency fund (or other funds that you might be needing to build such as your reserves and your float). And your float might be something that kind of develops naturally as a kind of monthly cash-cushion, and I am not even saying that it will take less than 6-12 months or maybe more just to get your emergency funds up to 3 months including building your bitcoin to a similar size and thereafter hopefully your bitcoin investment continues to grow based on a variety of circumstances, including your ongoing ability to be able to keep your discretionary income up by increasing your income and decreasing your expenses or whatever you deem to be within your abilities to accomplish.
You can accumulate aggressively with DCA after your emergency funds is upto 3 months to increase your bitcoin portfolio faster but don't overdo it. The size of your emergency funds is what the determine your level of aggressiveness.