To be pedantic, you probably can’t pay your mortgage on credit, or cash flow from paychecks if you lose your job.

Maybe I just come from an old school financial philosophy, but I don’t understand this aversion to being financially independent. The idea of someone making 6 figures but being completely reliant on the credit card company in an emergency is pretty wack.

The idea might be to maximize your expected wealth, e.g. if you consider this kind of emergencies as relatively unlikely and that even then you'd just have to pay interests on a credit card while you're recovering for a few months, it could be worth it to invest some of the money you currently have as an emergency fund into something other than cash.