Yeesh. Yes, you should have cash on hand for emergencies. Using credit cards for emergencies is the worst way to use them, and that's a big reason why the average US credit debt is $3500 or whatever.
You're thinking the wrong way.
I have maybe $2,000 in my checking account at any one time. The rest is in mutual funds and stocks. What if I have an auto accident and need to pay $4,500 to get my car fixed? I can't get the money out of my mutual funds / stocks for over a week. With a credit card though, I have 30-55 days (depending on when the purchase is within the billing cycle) to move money out and not have to worry.
If you literally have thousands in cash just sitting around in non-interest baring accounts, you aren't properly managing your financial assets.
Debit card transactions will get denied due to lack of funds, or I'll be hit huge with fees from the bank, if they even let it through.
Of course, I wouldn't get the $50 in 1.1% cash back either from the purchase either, so I just lost money.
Credit cards, if treated like cash can make you money.