Yeah. Any medical emergency I will not likely not know the actual cost for MONTHS afterward, any major home issues are likely known about well ahead of time and can be financed. Have a pile of cash in case of job lose sure I guess, but if I lost my job my monthly expenses would drop like a rock (no eating out, Target runs would dry up, put a hold on monthly ROTH contributions, only get the 36 pack of Bud Light instead of the "fancy" 24 pack of Sam Adams at Costco, etc.) - we are dual income and could squeak by on one income if needed.
So my E-fund is nothing. And everything.