For us, it makes more sense to have as much of our money we can being in the market or purchasing other assets. Between the two of us, and because we were really into travel hacking for points for a while, we have well into the six figures of open credit with some of it being at zero percent. If any emergency were to happen, we could easily use our cards up front to cover whatever we needed and then just sell off shares to get us even for a reasonable amount of time.
We keep $2,000 in a savings account to cover our homeowners and vehicle deductibles just in case. This makes DW feel a bit more safe to know that we have this amount, but I would honestly be ok with $0 cash knowing that deductibles can be paid on a credit card too.
Of course, it all depends on where you are in life and where your income is. We are both in stable careers in different fields making six figures, so the chance of us both losing our jobs and all of a sudden having zero income is a very unlikely possibility. If you are single, making lower income, or have a commission job that just makes ends meet I'd reconsider that strategy. We also don't have an issue racking up debt on credit cards and have never really had any personal debt like that. If you've struggled with things like that before it would be another reason to reconsider.
Realistically, whatever makes you sleep well at night. If you have a few extra thousand dollars sitting in a savings account, but stick to all other aspects of disciplined personal finance with even a modest income you will win in the end.