A couple of years ago, I followed the advice of several other MMM fans and transferred my emergency fund to a tax-advantaged investment account at Vanguard. In my case, this was a SEP IRA.
The logic made sense. It wasn't earning much of anything in a checking or savings account, so I should invest it instead. I've got my finances under control, so I have no need for an emergency fund. Those things are for novices.
Well, it didn't work out that well for me.
I lost a big client in late 2015 and had to swallow my pride and do grunt work for lower-paying companies before things picked back up. In my line of work, this sort of thing happens. During the few months I wasn't earning as much, I started getting nervous about not having cash around. I could access the money in my various tax-advantaged investment accounts, but I'd pay penalties and lose out on any gains (might even take on some unwanted losses).
I started to miss having easy access to cash in spite of the fact that it wouldn't be earning as much in a savings account as with VTSAX, et al. For me, the best solution was to reestablish my emergency fund. As soon I picked up some more work and started earning a little more money, I stuffed it in the savings account at my credit union. I started feeling less anxious once the account balance hit $5K. Once it got to $10K, I stopped adding to savings and started contributing extra cash to investments again.
My situation isn't typical. I'm self-employed and have irregular, unpredictable income. I don't have a secure job with a high salary and an employer who desperately needs me. If I did, I might not need the emergency fund. But, alas...
Anyway, that's just my $0.02 (or $10K?) on the emergency fund "issue." Liquidity helps me sleep better at night.