I don't understand why we still mint a $100. It's the prime counterfeiting target, is mostly used overseas, and is too big for real commercial value. It seems like just having the $20 be the largest bill would overcome all these problems.
The article says: "The most recent statistics from the Fed show that as of Dec. 31, there were 10.3 billion $1 bills, in circulation, 8.6 billion $100 bills and 7.4 billion $20 bills, followed by $5's, $10's, $50's and $2's. A little more than 75% of the more than $1 trillion of currency in circulation is in $100 bills. Much of it is held outside the United States." If we switched to 20s, we'd need 43 billion more 20s.
$100s have plenty of commercial value. Any time you're exchanging physical things of high value, cash is key. Cashiers checks, etc., can and are forged. Also, gamblers regularly walk around with 10s of thousands of dollars on them.
That's one thing I like about Danish money; the 500 kr note (~$90) and 200 kr note (~$35) are both common and regularly used. Makes it much more convenient to use cash for things like groceries or restaurants without having to carry around a thick wallet full of wads of $20s. Sure, many people use cards too, but you don't have to if you prefer cash.
The greatly increased CoL in Denmark also somewhat necessitates the prevalence of larger denominations.
I don't find much difference in CoL between the Bay Area and Copenhagen. If anything it's slightly cheaper in Denmark (more expensive restaurants, but cheaper rent). If you're comparing median U.S. CoL, sure, but even in high-CoL areas like San Francisco and New York City, $100 bills seem rare, despite the fact that >$100 tabs at NYC restaurants are not exactly rare. The difference seems to be that Americans are wary of larger amounts of cash, so use a card for anything nontrivial (or among older people, a personal check), while Danes can go either way, depending on personal preference. I'd blame it on the difference in mugging rates, probably.
The highest denomination in China is 100 yuan (you can think of it like a $20, though it's worth slightly less). People here pay rent in cash. It drove me nuts when I had to pay 12000 yuan of rent in 120 small bills. My landlord even asked "is it the correct amount?" -- I have no idea; I'm trusting the bill-counting machine at the bank!
You want it to be used overseas. It's a free loan.