At some point in time when we are depleting so many of our various back up funds and/or reserve funds, then all that we end up having remaining is our emergency funds, and at some point, we cannot buy bitcoin anymore with those funds.. since we hardly have any money left and we are down to the bare morsels and we will run out of whatever we have soon..
I tend to think that once we get to our emergency funds, our status/situation is devolving so badly that it is possible that we are going to end up having to start to sell from our bitcoin since our emergency funds are getting close to running out.. so it does not seem to make any sense by the time we get down to only having emergency funds to continue buying bitcoin with our soon to be depleted funds.. especially if we have a lot of uncertainty regarding the timing or the amount of our next incoming funds...
I also think that the duration at which you build your emergency funds particularly to sustain your expenses should also depend on the worst case scenario of income arrival fluctuations. I have had a situation whereby my salary was delayed for four months at my place of work(due to some leadership transition issues, but it was eventually paid), so I made it a point of duty to build my emergency funds up to 6 months of my expenses to create a tolerance for the scenario I experienced earlier and in a bid not to ever touch my portfolio in such cases and beyond that to give me more tolerance to get hooked up with another source of income if my previous source gets cut off without prior information.
I think for me 6 months is a very good timeframe to fix my finances in case of anything unpleasant happens as against just 3 months, reason I built my emergency funds to my comfort timing.