Here in the United Kingdom, the largest bank note in common use is the £20. You would need five of them to pay for a cheap hotel room in central London and ten to pay for a moderately expensive one. A £50 note exists but is not in common use. Present one to pay for goods and both you and the bank note will be subject to very suspicious scrutiny. Normal people don't have £50 notes. In reality, most £50 notes have left the country. They are in Poland where they have been remitted by Polish workers in the UK.
In contrast, the UK groans under the weight of small coins - the 1p, 2p, 5p - which are kept in circulation as if there has been zero price Inflation since they were introduced over 40 years ago. You would need 200 penny coins to take out a coffee from a cheap chain coffee shop. You would need 250 coins to buy the daily newspaper I read (The Financial Times).
In €uroland, the 50€ note is in common use - at today's rate, it's worth £42.30. In the supposedly poor ex- Soviet Bloc Czech Republic, the 1000 Koruna note is in general use. That's £32.70.
So why does the UK not have cash in appropriate denominations, freely available and accepted?
The short answer is: the Banks. They find it cumbersome and expensive to handle cash, to take it in and to hand it out. But they make money when you use their debit cards and credit cards to pay for purchases. So do the credit card companies. As a result, we have a very big Lobby which would like to move us into a "cashless economy".And they want us to pay for it. And they don't care how irritating it is to stand in a queue while someone pays for their cigarettes or their bottle of milk with a card.
Then there are the Retailers. They don't want cash on their premises because it can be stolen. Fair enough. Perhaps more importantly, if you pay by card - and especially if you combine your credit card with their Loyalty card - then they can study your spending habits and target you accordingly.
Retailers are probably more interested in your spending habits than the NSA is in your emails.
Of course, there are other groups interested in your spending habits, notably criminals trying to steal your credit card or, nowadays, just the necessary name and numbers.
So we have two (or three if you count the criminals) powerful Lobbies opposed to what could be a fast and convenient way of paying - which is what Cash is.
If you want to make the Case for Cash, just start using it. Especially the £50 notes. And when they give you 1p, 2p and 5p coins in your change - well, just hand them back or drop them in the Charity box beside the till. If enough people refused these coins, it would force them out of circulation.