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I don’t have a disaster fund or an emergency fund. For emergencies, I use a credit card. Why do I do that? The reason is that emergency funds must sit in a checking account to be liquid. While sitting there they earn less than a savings account (in general) typically only a few percent.
If I use a credit card, I will have a 20 grace period during which I do not pay interest. This gives me sufficient time to move money from my savings account or my broker account into the checking account from where I can pay off the credit card. This way I am not losing money from money gathering dust in a checking account.

I would still do it even if I carried a balance on my credit cards. Suppose the credit limit is $6000, the debt is $4000 and the hypothetical emergency fund is $2000. Also assume 20% interest on the debt, and 4% interest on fund. The total interest expense on the debt is ($800) and the interest income on the fund is $80 leaving a net negative of ($720). The amount of liquidity is $2000 from the credit card and $2000 from the fund for a total of $4000.

Now put the $2000 of the fund towards paying off the debt. Then the credit limit is $6000, the debt is $2000 and the hypothetical emergency fund is $0. Also assume 20% interest on the debt, and 4% interest on fund. The total interest expense on the debt is ($400) and the interest income on the fund is $0 leaving a net negative of ($400). This is $320 more cash in your hand than with the emergency fund. The amount of liquidity is $4000 from the credit card and $0 from the fund for a total of $4000 like before.

There is one instance where I would carry an emergency fund. If I had no credit I would create an emergency fund. In fact in that case a fund becomes crucial as it avoids payday loans (which I would never touch unless I had a job) and cash checking loans, which to me seems like a desperate way of getting credit that one might only use once or twice during a lifetime.