I'm old enough that I could start drawing from IRAs whenever I want to...so that's my "emergency" account. TlofML is in his 50's, and I've been badgering him to get his EF out of the savings acct that pays less than 0.5% interest...he knows he needs to, but hasn't yet gotten off the dime to do it.
That said, it seems to me that, whether you are my age, or in your 20's, you need to define two really important criteria for yourself.
1: What is an emergency? and
2: How much do I need in case of that emergency?
As Haley's scenario with her parents demonstrates, an emergency that becomes chronic is no longer an emergency on its own, and may foment further issues, if not handled properly from the beginning.
I would posit that MSing as an EF is a fine example such "not handling properly" from the beginning. Losing your job is a real and, for nearly all of us, likely possibility at some point in our lives. I spent the final 8 years of my employment life working for small corporations. I worked for four, and was laid off from three. At that point, I became a full time entrepreneur, with my very own set of challenges. Had I bought $20K in gift cards, something I could easily have done with available credit, I would have just added to the pressure, not relieved any of it.
Assuming that your plan is to be re-employed at some point, even a fully stocked 6 months of income EF can be insufficient, if the economy is in the state it was in 2009. Once the unemployment insurance runs out, you are completely dependent on that fund. And the chances that, once you actually find a new job, that it will pay what the old one did, are not fantastic.
I don't like to define savings as EFs, myself. To me, anytime that expenses stay consistent, and income drops, or income stays consistent, and expenses rise, is a time to think about those savings and using part of them, even knowing they'll need to be replaced when the crisis is past.
A dead oven, a week before Thanksgiving? You may have budgeted for Christmas, but not that extra $1K for the oven. Taking the funds from the EF, and replacing them in the next two to three months makes better sense to me than to let interest accrue on the cost of the oven. You'll lose less on that $1K, no matter where it's stashed, than you'd pay in interest on it, even for a month.