Emergency funds are good for (1) lower income people, and (2) people who are just starting out and still have financially irresponsible habits.
For everybody else, an emergency fund is just making you poorer.
And what about when you lose your job during a market crash, forcing you to sell your investments at a substantial loss?
If that's what you're trying to protect against, even a 6 month emergency fund won't last you through the crash. If you still don't have a job after 6 months, you will have to sell some of your portfolio.
This seems more like an argument to not be 100% stocks, than it is to have a cash emergency fund. But even if you were 100% stocks, and your portfolio dropped 50%, as Cathy mentioned, you'd only be losing 50% on the portion you had to sell. So if you had to sell $18,000 for six months of expenses, and stocks were down 50%, that would have cost you an additional $18,000. Since money in the stock market is expected to double every 7-10 years or so, that limits your risk of loss to that timeframe.
In other words, if your $18,000 investment has more than doubled, you'll be ahead by investing. In that sense, a cash emergency fund really has a limited shelf-life of usefulness. And that's the worst case 100% stocks scenario. If you have bonds in your portfolio, you'll be just fine.
If your stock fund drops by half, and you need $18,000, you just take it from your bonds:
If your bond fund drops by half (hasn't ever happened, but for illustration purposes), you just take it from stocks:
That's the best part about diversification across uncorrelated asset classes. It's unlikely they will both drop at the same time :)