I've seen several questions (e.g. here) that challenge the need for complete liquidity in an emergency fund. Answers often focus not just on the potential for market downturns to affect your ability to liquidate assets, but even the 2-3 day delay in fund availability being a potential disaster. However, I cannot think of any real-world situation in which this time sensitivity could actually be the case, and no answer that I've seen so far offers any examples.
A year after my bankruptcy in my much younger days I was approved for a credit card with no annual fee and a $3,000 limit. Within a year I was at $10,000. So if someone with bad credit, only 2 years post-bankruptcy, can attain $10,000 in unsecured credit, I imagine most anyone can. As such, home repairs, car repairs, medical expenses, and most anything else can be put on credit for up to 30 days with no interest, which is far longer than is needed to liquidate any kind of stock or mutual fund. And beyond $10,000 also pushes the limits of 3-6 months of salary for many. Yes, I'm assuming that anyone with enough forethought to use an emergency fund would also have their credit cards completely paid off.
Assuming a credit card cannot be used, or for some reason cannot be attained, what sort of emergency requires payment up front for which 2-3 days processing of a stock sale would pose a problem? Any home repairs and car repairs I've had done allow a few days for payment, or accept a personal check at the end of the job (which will often take 2-3 days). All medical bills I've received appear after insurance has processed them, which can take 30 days or more. Short of owing money to the mob, or a zombie apocalypse, what sort of emergency could require immediate liquidity of an emergency fund.
For the purposes of this question I wish to understand only the need for immediate liquidity. Issues with market volatility are a separate discussion.